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COMPENDIUM OF METEOROLOGY 



h 



COMPENDIUM 



OF 



METEOROLOGY 



Prepared under the Direction of the 

Committee on the Compendium of Meteorology 

H. R, BYERS H. E. LANDSBERG H. WEXLER 

B. HAURWITZ A. F. SPILHAUS H. C. WILLETT 

H. G. HOUGHTON, Chairman 



Edited by 

THOMAS F. MALONE 




AMERICAN METEOROLOGICAL SOCIETY 

BOSTON, MASSACHUSETTS 

1951 



COPYRIGHT 1951 BY THE 
AMERICAN METEOROLOGICAL SOCIETY 
All rights reserved. This book, or 
parts thereof, may not be reproduced 
without the permission of the pub- 
lisher and the sponsoring agency. 



COMPOSED AND PRINTED AT THE 

WAVERLY PRESS, INC. 

BALTIMORE, MD.. U.S.A. 



PREFACE 

The purpose of the Compendium of Meteorology is to take stock of the present position of meteorology, to sum- 
marize and appraise the knowledge which untiring research has been able to wrest from nature during past years, 
and to indicate the avenues of further study and research which need to be explored in order to extend the frontiers 
of our knowledge. Perhaps it is appropriate that this stocktaking should be made as we enter the second half of 
the twentieth century, for surely no one can read the pages which follow without experiencmg the feeling that 
we are on the threshold of an exciting era of meteorological history in which significant advancements are possible 
toward a better understanduig of the physical laws which govern the workings of the atmosphere. That this progress 
will not be made without some difficulty is quite apparent from the number of unsolved problems which still 
remain as a challenge to the research worker in spite of the centuries of study which have been devoted to the 
nature and behavior of the atmosphere. If this book will have clarified and defined these problems, it will have 
fulfilled the purpose of those who planned it. 

The desirability of a survey of the current state of meteorology became apparent during the years following 
World War II, when research effort was being greatly intensified not only in meteorology but also in other fields 
of pure and applied science in which the importance of meteorological factors was coming into recognition. The 
idea that meteorologists and atmospheric physicists from all over the world might combine their efforts to prepare 
a work of this nature took definite shape in 1948 when the Geophysics Research Division of the Air Force Cam- 
bridge Research Center invited the American Meteorological Society to draw up plans for a book in which special- 
ists in the several fields of meteorology would appraise the state of knowledge in their respective specialties. The 
general scope of the work was decided upon by representatives of the Society and the Geophysics Research Divi- 
sion, and support and sponsorship was provided by the latter under Contract No. W 28-099 ac-399 with the So- 
ciety. It is understood, however, that the recommendations and conclusions presented in the articles which follow 
do not necessarily represent those of the sponsoring agency. 

Capt. H. T. Orville, U.S.N. (Ret.), president of the Society from 1948 to 1950, appointed the Committee on 
the Compendium of Meteorology, under the chairmanship of Professor H. G. Houghton, to organize and supervise 
this undertaking. This committee sought and obtained suggestions from many eminent meteorologists and, in a 
series of meetings in the latter part of 1948, formulated the specific nature of the present work. One hundred and 
two authors were commissioned in 1949 to prepare the one hundred and eight articles which comprise this book. 
In most cases, more than one author was invited to contribute on a single broad topic. This was done intentionally, 
despite some slight duphcation, to uisure the presentation of specialized aspects of certain general subjects and to 
provide ample opportunity for the exposition of different viewpoints. 

A logical grouping of papers on related topics has resulted in a division of the book into twenty-five sections. 
Since the composition and physics of the atmosphere are fundamental to a consideration of meteorological prob- 
lems, the first part of the book is concerned with the field generally referred to as physical meteorology. Then comes 
a discussion of the upper atmosphere — a topic in which the interests of meteorologists and physicists are now con- 
verging — followed by a section which deals with extraterrestrial effects on the atmosphere and with the meteorology 
of other planets. The section in which is presented a general discussion of the dynamics of the atmosphere is fol- 
lowed by three sections which treat various aspects of the primary, secondary, and tertiary circulations, respec- 
tively. These papers provide a logical introduction to the treatment of synoptic meteorology and weather fore- 
casting and to the discussions of the meteorology of the tropical and polar regions and the section on climatology. 
Hydrometeorology, marine meteorology, biological and chemical meteorology, and atmospheric pollution are fields 
in which the interests of meteorologists meet those of hydrologists, oceanographers, biologists and chemists, and 
engineers, and these topics are treated in that order. The topics of clouds, fog, and aircraft icmg have been in- 
cluded in a single section because of their obvious relationship to one another. The discussions of meteorological 
instruments and laboratory investigations and the theory of radiometeorology and microseisms and their applica- 
tions to meteorological problems constitute the final sections. 

References to the literature are indicated by bracketed nimabers in the text. A fist of references is given at the 
end of each article. Some care has been exercised to insure complete and accurate bibhographic information. Ab- 
breviations for the titles of periodicals have, with a few minor modifications, followed the convenient system used 
in the second edition of A World List of Scientific Periodicals, pubUshed by the Oxford University Press in 1934. 
When successive entries have one or more authors in common, dashes have been used to replace the name, or 
names, given in the preceding entry. 
It is a pleasure to acknowledge the interest and cooperation, quite apart from the financial support, of the Geo- 



vi PREFACE 

physics Research Division in this undertaking. The Division's Ubrary was kindly made available for use in the 
editorial work and the friendly counsel and suggestions of Division personnel have been most helpful. Sincere ap- 
preciation is due to Professor Hans Neuberger for carefully checking and editing the papers translated from the 
German. Miss Eleanor Richmond and Mr. W. Lawrence Gates have labored long and faithfully in systematizing 
and checking the Usts of references and in assisting with the editing and proofreading. The assistance of Mr. Jean 
Le Corbeiller in the editorial work and proofreading is also gratefully acknowledged, as is the careful proofreading 
by Mrs. William Greene and Mrs. Israel Kopp. Mr. Kenneth C. Spengler, executive secretary of the American Mete- 
orological Society, his assistant, Mrs. Holt Ashley, and their staff have capably handled all of the administrative 
matters connected with this work. Preparation of the illustrations for publication has been efficiently accomplished 
by Mr. Chester Jancewicz. 

BOSTON, MASSACHUSETTS - T. F. M. 

August 1951 



TABLE OF CONTENTS 

COMPOSITION OF THE ATMOSPHERE 

The Composition of Atmospheric Au- by E. Glueckauf 3 

RADIATION 

Solar Radiant Energy and Its Modification by the Earth and Its Atmosphere hj Sigmund Fritz 13 

Long-Wave Radiation by Fritz Moller ~ 34 

Actinometric Measurements by Anders Angstrom 50 

METEOROLOGICAL OPTICS 

General Meteorological Optics by Hans Neuberger 61 

Polarization of Skylight by Zdenek Sekera 79 

Visibility in Meteorology by W. E. Knowles Middleton 91 

ATMOSPHERIC ELECTRICITY 

Universal Aspeette of Atmospheric Electricity by 0. H. Gish 101 

Ions in the Atmosphere by G. R. Wait and W. D. Parkinson 120 

Precipitation Electricity by Ross Gunn 128 

The Lightning Discharge by J. H. Hagenguth 136 

Instruments and Methods for the Measurement of Atmospheric Electricity by H. Israel 144 

Radioactivity of the Atmosphere by H. Israel 155 

CLOUD PHYSICS 

On the Physics of Clouds and Precipitation by Henry G. Houghton 165 

Nuclei of Atmospheric Condensation by Christian Junge 182 

The Physics of Ice Clouds and MLxed Clouds by F. H. Ludlam 192 

Thermodynamics of Clouds by Fritz Moller 199 

The Formation of Ice Crystals by Ukichiro Nakaya 207 

Snow and Its Relationship to Experimental Meteorology by Vincent J. Schaefer 221 

Relation of Artificial Cloud-Modification to the Production of Precipitation by Richard D. Coons and Ross Gunn 235 

THE UPPER ATMOSPHERE 

General Aspects of Upper Atmospheric Physics by S. K. Milra 245 

Photochemical Processes in the Upper Atmosphere and Resultant Composition by Sidney Chapman 262 

Ozone in the Atmosphere by F. W. Paul Gqtz 275 

Radiative Temperature Changes in the Ozone Layer by Richard A. Craig 292 

Temperatures and Pressures in the Upper Atmosphere by Homer E. Newell, Jr 303 

Water Vapour in the Upper Air by G. M. B. Dobson and A W. Brewer 311 

Diffusion in the Upper Atmosphere by Heinz Lettau 320 

The Ionosphere by S. L. Seaton 334 

Night-Sky Radiations from the Upper Atmosphere by E.O. Hulburt 341 

Aurorae and Magnetic Storms by L. Harang • • • • 347 

Meteors as Probes of the Upper Atmosphere by Fred L. Whipple 356 

Sound Propagation in the Atmosphere by B. Gutenberg 366 

COSMICAL METEOROLOGY 

Solar Energy Variations As a Possible Cause of Anomalous Weather Changes by Richard A. Craig and H. C. Willett. ... 379 

The Atmospheres of the Other Planets by S. L. Hess and H. A. Panofsky 391 

DYNAMICS OF THE ATMOSPHERE 

The Perturbation Equations in Meteorology by B. Haurwitz 401 

The Solution of NonUnear Meteorological Problems by the Method of Characteristics by John C. Freeman 421 

Hydrodynamic Instability by Jacques M. Van Mieghem 434 

Stability Properties of Large-Scale Atmospheric Disturbances by R. Fj^rtoft 454 

vii 



viii TABLE OF CONTENTS 

The Quantitative Tlieory of Cyclone Development by E. T. Eady 464 

Dynamic Forecasting by Numerical Process by J. G. Charney 470 

Energy Equations by James E. Miller 483 

Atmospheric Turbulence and Diffusion by 0. 0. Sutton 492 

Atmospheric Tides and Oscillations by Sydney Chapman 510 

Application of the Thermodynamics of Open Systems to Meteorology by Jacques M. Van Mieghem 531 

THE GENERAL CIRCULATION 

The Physical Basis for the General Circulation by Victor P. Starr 541 

Observational Studies of General Circulation Patterns by Jerome Namias and Philip F. Clapp 551 

Apphcations of Energy Principles to the General Circulation by Victor P. Starr 568 

MECHANICS OF PRESSURE SYSTEMS 

Extratropical Cyclones by J. Bjerknes 577 

The Aerology of Extratropical Disturbances by E. Palmen ; 599 

Anticyclones by H. Wexler 621 

Mechanism of Pressure Change by James M. Austin 630 

Large-Scale Vertical Velocity and Divergence by H. A. Panofsky ; . . . . 639 

The Instabihty Line by J. R. Fulks 647 

LOCAL CIRCULATIONS 

Local Winds by Friedrich Defant 655 

Tornadoes and Related Phenomena by Edward M. Brooks 673 

Thunderstorms by Horace R. Byers 681 

Cumulus Convection and Entrainment by James M. Austin 694 

OBSERVATIONS AND ANALYSIS 

World Weather Network by Athelstan F. Spilhaus 705 

Models and Techniques of Synoptic Representation by John C. Bellamy 711 

Meteorological Analysis in the Middle Latitudes by V. J. Oliver and M. B. Oliver 715 

WEATHER FORECASTING 

The Forecast Problem by H. C. Willett 731 

Short-Range Weather Forecasting by Gordon E. Dunn 747 

A Procedure of Short-Range Weather Forecasting by Robert C. Bundgaard 766 

Objective Weather Forecasting by R. A. Allen and E. M. Vernon 796 

General Aspects of Extended-Range Forecasting by Jerome Namias 802 

Extended-Range Weather Forecasting by Franz Baur 814 

Extended-Range Forecasting by Weather Types by Robert D. Elliott 834 

Verification of Weather Forecasts by Glenn W. Brier and Roger A. Allen 841 

Application of Statistical Methods to Weather Forecasting by George P. Wadsworth 849 

TROPICAL METEOROLOGY 

Tropical Meteorology by C. E. Palmer 859 

Equatorial Meteorology by A. Grimes 881 

Tropical Cyclones by Gordon E. Dunn 887 

Aerology of Tropical Storms by Herbert Riehl 902 

POLAR METEOROLOGY 

Antarctic Atmospheric Circulation by Arnold Court 917 

Arctic Meteorology by Herbert G. Dorsey, Jr 942 

Some Climatological Problems of the Arctic and Sub-Arctic by F. Kenneth Hare 952 

CLIMATOLOGY 

Climate— The Synthesis of Weather by C. S. Durst 967 

Applied Climatology by Helmut E. Landsberg and Woodrow C. Jacobs -. 976 

Microclimatology by Rudolf Geiger 993 



TABLE OF CONTENTS ix 

Geological and Historical Aspects of Climatic Change by C. E. P. Brooks 1004 

Climatic Implications of Glacier Research by Richard Foster Flint 1019 

Tree-Ring Indices of Rainfall, Temperature, and River Flow by Edmund Schulman 1024 

HYDROMETEOROLOGY 

Hydrometeorology in the United States by Robert D. Fletcher 1033 

The Hydrologic Cycle and Its Relation to Meteorology — River Forecasting by Ray K. Linsley 1048 

MARINE METEOROLOGY 

Large-Scale Aspects of Energy Transformation over the Oceans by Woodrow C. Jacobs 1057 

Evaporation from the Oceans by H. U. Sverdrup 1071 

Forecasting Ocean Waves by W. H. Munk and R. S. Arthur 1082 

Ocean Waves as a Meteorological Tool by W. H. Munk 1090 

BIOLOGICAL AND CHEMICAL METEOROLOGY 

Aerobiology by Woodrow C. Jacobs 1103 

Physical Aspects of Human Bioclimatology by Konrad J. K. Buettner 1112 

Some Problems of Atmospheric Chemistry by H. Cauer 1 1 26 

ATMOSPHERIC POLLUTION 

Atmospheric Pollution by E. Wendell Hewson 1139 

CLOUDS, FOG, AND AIRCRAFT ICING 

The Classification of Cloud Forms by Wallace E. Howell : 1161 

The Use of Clouds in Forecasting by Charles F. Brooks 1167 

Fog by Joseph J. George 1179 

Physical and Operational Aspects of Aircraft Icing by Lewis A. Rodert 1190 

Meteorological Aspects of Aircraft Icing by William Lewis 1197 

METEOROLOGICAL INSTRUMENTS 

Instruments and Techniques for Meteorological Measurements by Michael Ference, Jr 1207 

Aircraft Meteorological Instruments by Alan C. Bemis 1223 

LABORATORY INVESTIGATIONS 

Experimental Analogies to Atmospheric Motions by Dave Fultz 1235 

Model Techniques in Meteorological Research by Hunter Rouse 1249 

Experimental Cloud Formation by Sir David Brunt 1255 

RADIOMETEOROLOGY 

Radar Storm Observation by Myron G. H. Ligda 1265 

Theory and Observation of Radar Storm Detection by Raymond Wexler 1283 

Meteorological Aspects of Propagation Problems by H. G. Booker 1290 

Sferics by R. C. Wanta 1297 

MICROSEISMS 

Observations and Theory of Microseisms by B. Gutenberg 1303 

Practical Application of Microseisms to Forecasting by James B. Macelwane, S. J 1312 

Index 1317 



COMPOSITION OF THE ATMOSPHERE 

The Composition of Atmospheric Air by E. Glueckauf 3 



THE COMPOSITION OF ATMOSPHERIC AIR 

By E. GLUECKAUF 
Atomic Energy Research Establishment, Harwell, England 



For many reasons it is desirable to have a complete 
knowledge of the composition of the atmosphere as 
regards both the molecular species present and their 
absolute quantities. This applies not only to the main 
components, but also to rare species of polyatomic 
molecules whose importance in the radiation balance 
is often quite out of proportion to their actual quantity. 
Any observed variation in the composition of air — with 
time, with geographical location, with height, with the 
seasons, or with meteorological conditions — seriously 
affects our conception of the processes in the atmos- 
phere. It follows from this that the present article must 
lay its emphasis on facts in order to see where our 
knowledge is still inadequate. 

SURVEYS OF VARIATIONS IN THE 

COMPOSITION OF THE 

ATMOSPHERE 

Oxygen (O2). The first "international" investigation 
of the O2 content with adequate equipment was carried 
out as early as 1852 by Regnault [18] (see Table I). 
He concluded that atmospheric air presents only small 
variations. 

Table I. Sukvet of Oxtgbn Content 
(After Regnault [18]) 



Location 


Average O2 (per cent) 


Montpellier 


20 95 ± 00 


Lyon 


20 94 ± 01 


Normandy 


20.95 


Berlin 


20 96 ± 01 


Mediterranean* 


20.94 ± 0.01 


Atlantic 


20 94 ± 01 


East Indian Ocean 


t 


Arctic Ocean 


20.91 ± 0.01 


Paris 


20 96 ± 0.01 






Average 


20.944 







* Two samples from Algiers have been omitted, 
t Greatly varying, mostly low. 

Sixty years later, in a survey involving many hun- 
dreds of precision analyses, Benedict [c. 16]' proved 
conclusively that during a period of about two years, 
which involved a great variety of weather conditions, 
no material variations occurred in the O2 content of 
air at the Nutrition Laboratory of the Carnegie Insti- 
tution of Washington. A statistical analysis of Bene- 
dict's data gives a standard deviation of ±0.006 per 
cent, while the repeated analysis of a bottled air sample 
gave a standard deviation of only ±0.0025 per cent. 
It is likely that the higher standard deviation of the 



that detailed reference is given in the paper cited. 



former originated from minute variations in the sam- 
pling procedure. 

Similar precision was obtained by Krogh [c. 16] 
whose analyses from October 4, 1917, to January 25, 
1918, showed a standard deviation of ±0.005 per cent 
for O2, ±0.0025 per cent for CO2, and ±0.0020 per 
cent for O2 plus CO2, all in uncontaminated air. The 
absolute values for O2 and CO2 in dry air obtained by 
Krogh after careful calibrations are shown in Table II. 
This last figure — or the corresponding figure of 79.0215 
per cent for the content of "atmospheric nitrogen" 
{i.e., N2 + rare gases) — is considered by Krogh to be 
a geophysical constant which does not vary more than 
indicated by the standard deviation observed (±0.0020 
per cent). 

Table II. Oxygen and Carbon Dioxide Values in Dry Air 
(After Krogh [c. 16]) 



Constituent 


Content (per cent) 




Experiment I 


Experiment II 


CO, 

O2 


0.0305 
20.9480 


0.0300 
20.9485 






O2 + CO2 


20.9785 


20.9785 







The absolute value of the O2 content of air obtained 
by Benedict, taking into account a small correction 
resulting from the formation of CO from the pyrogal- 
late, was later computed by Benedict and by Haldane 
as 20.952 per cent and by Krogh [c. 16] as 20.954 per 
cent. 

While Benedict's experiments prove conclusively that 
only trifling changes occur in air observations at one 
locality, it is more difficult to show that there is uni- 
formity over all the earth's surface. For such a survey 
it is necessary to bottle air samples, and changes of one 
or two parts in ten thousand can easily occur during 
transit of the air sample. Table III gives a summary of 
Benedict's analyses of air of various origins. It is not 

Table III. Survey of Oxygen Contents 
(After Benedict [c. 16]) 



Origin of air 



Boston, Mass 

Ocean air (Montreal to Liverpool). 

Ocean air (Genoa to Boston) 

Pikes Peak* 




O, 
(corrected) 
(per cent) 



20.952 
20.950 
20.946 
20.945 



* The data for August 14, 1911 which showed abnormally 
low values have been omitted. 

likely that significance can be attached to these small 
variations. 



COMPOSITION OF THE ATMOSPHERE 



An oxygen deficiency in antarctic air, claimed by 
Lockhart and Court [c. 12], cannot yet be regarded as 
well established, since no check analyses with normal 
air were carried out. 

In spite of Paneth's conservative estimate [16] that 
the second decimal is still not exactly known, the author 
feels inclined, in view of the agreement of the two best 
surveys with a recent redetermination by M. Shepherd 
[c. 16] which gave 20.945 per cent, to recommend an 
absolute value of 20.946 ± 0.002 per cent as the most 
likely figure for the O2 content of uncontaminated air, 
in combination with an average CO2 value of 0.033 per 
cent. 

Apart from possible minor changes resulting from 
the greater solubility of O2 than of A''2 in ocean water, 
all major variations of the O2 content must result 
from the combustion of fuel, from the respiratory ex- 
change of organisms, or from the assimilation of CO2 in 
plants. The first process does not result in more than 
local changes of the O2 content, while the latter two 
processes, though locally altering the CO2/O2 ratio, 
leave their sum unchanged. 

Carbon Dioxide (CO2). Though the extensive in- 
vestigations of Benedict and of Krogh suggest that the 
CO2 content of atmospheric air over land does not vary 
except within very narrow limits, significant variations 
of the CO2 content have been observed by workers 
both before and after them. 

In particular, Callendar [5] has dra\vn attention to 
an increase in the CO2 content during the last fifty 
years which is best demonstrated in Fig. 1. This in- 



330 




o 

o 290 



I860 1900 1925 1950 

Fig. 1. — Increase of COt in air. (After Callendar [5].) 

crease in the total atmosphere of about 30 ppm (parts 
per miUion) represents a quantity of CO2 (2 X 10 '' 
tons) which is approximately equal to the amount re- 
sulting from the combustion of fuels produced during 
this period. This implies that not much of this excess 
CO2 has been lost to the ocean water, an assumption 
which is justified in view of the fact that, apart from a 
thin agitated surface layer, the transport of CO2 inside 
the water proceeds by diffusion and is very slow. 

Variations of the CO2 Content over the Sea. The vari- 
ations of CO2 over the sea are now well understood 
(Buch, Wattenberg [c. 5]). Because of an excess of 
strongly basic cations over strongly acid anions in sea 
water, CO2 is soluble in sea water not only as dis- 
solved CO2, but also in the form of carbonate and bi- 



carbonate ions, the quantities being roughly of the 
order 1:8:150. The result of this is that one litre of sea 
water contains about 150 times as much CO2 as the 
same volume of air. 

For a given content of total CO2, the equilibrium 
pressure varies considerably with the water tempera- 
ture. To give an example: For water with a chloride 
content of 1.95 per cent and a total CO2 of 2.07 X 10~' 
mol 1~\ the CO2 pressures^ in air at equilibrium at 
OC, IOC, 20c, and 30C are 1.6, 2.5, 3.6, and 5.1 X 
10~* atm, respectively. Thus, far from having an equal- 
izing effect on the CO2 content of the air, as was be- 
lieved during the last century and the earlier part of 
this century, changes in the surface temperature of the 
sea upset the otherwise comparatively constant CO2 
content of air. This explains the low values of the CO2 
content found near the polar regions. The lowest value 
(1.52 X 10^* atm) was observed near Spitsbergen by 
Buch [c. 5]. This value corresponds roughly to the 
equilibrium value at OC. 

In the most northerly regions, particularly over polar 
ice, the CO2 content is again normal, a feature which 
was explained by Buch on the basis of Bjerknes' scheme 
of the air circulation over the Atlantic. According to 
the latter, air in the Arctic is more or less constantly 
descending, and since it has by-passed at great height 
the .cold-water regions on its way from the south, its 
CO2 content would be expected to be near that of the 
temperate zones. Buch found 2.57 and 2.91 X' 10"* 
atm. 

Equally complicated is the situation in regions where 
masses of water rise to the surface from greater depths. 
The CO2 content of sea water, after falling slightly in 
the first 50 m below the surface (due to CO2 assimila- 
tion) , rises to a maximum at about 500-m depth where 
the CO2 pressure may be as much as 11 X 10~* atm 
(obviously due to decay of organic matter). If these 
C02-rich water masses rise to the surface (as observed 
near the west coast of Africa), the CO2 content of air 
may locally rise to 7 X 10"* atm. Similarly high values 
have been observed by Krogh [14] in the vicinity of 
West Greenland, and by Moss [c. 14] at latitude 
82°27'N, though in these two cases the origin of the 
CO2 was not traced, and the effect may possibly, but 
not necessarily, be spurious. 

These phenomena apparently do not affect the air 
masses to a very great depth. Near Petsamo, Finland, 
arctic air (range 297 to 313 ppm) differs unmistakably 
from continental and tropical air (range 319 to 335 
ppm), so that in this region the CO2 content can serve 
as an indicator for the origin of the air masses. How- 
ever, these differences become smaller as we go farther 
south. Thus the difference is still appreciable at Kew, 
England, where, on the average, subtropical air con- 
tains 19 ppm more CO2 than polar and maritime air; 
but the mean difference is only 8 ppm near Dieppe, 
France, and Gembloux, Belgium [c. 5]. 



2. The CO2 pressure in atmospheres is very nearly, but not 
quite, identical with the "parts per volume" unit, i.e., 10~^ 
atm !~ 100 ppm. 



THE COMPOSITION OF ATMOSPHERIC AIR 



The contaminations of CO2 caused by large towns 
are also fairly localised. At Kew, about 6 miles west 
of the centre of London, on the average only 27 ppm 
more CO2 are found in easterly than in westerly winds. 

Argon {A). The constancy of the composition of air 
with respect to its minor constituents has been investi- 
gated in the cases of A and He. The former was in- 
vestigated by Moissan [c. 16], who, after chemical 
removal of O2, A'^2, and CO2 by calcium metal, measured 
the remaining rare gases and obtained for the A content 
the figures shown in Table IV. The standard deviation 
of these analyses (excepting the value of 0.949 over 
the Atlantic Ocean which must be considered errone- 
ous) is ±0.002 per cent, or 0.2 per cent of the A con- 
tent, and within these limits there are no significant 
variations. 

Table IV. Survet op Argon Contents of Air 
{After Moissan [c. 16]) 



Location 


A (per cent) 


Odessa 


0.935 




0.933 


Athens 


0.935 


Ionian Sea (37°N, 15°E) 


0.936 




0.938 


Berlin 


0.932 




0.936 


Mt. Blanc 


0.935 




0.934 




0.933 


Atlantic Ocean (37°N, 24 °W). . 


0.932 


Atlantic Ocean (43°N, 22°W) 


(0.949) 


Average (omitting the last value) .... 


0.9343 ± 0.0006 



Helium {He) . Similar results were also obtained with 
He in spite of the fact that vast quantities of He 
constantly escape from the earth's crust, particularly 
from oil fields in the United States. It has been esti- 
mated that between eight and thirty million cubic 
metres of He are generated annually by radioactive 
processes. The amounts of He added to the atmosphere 
in this way are balanced by losses of He into the void 
of the universe, because He, owing to its lightness, is 
not permanently retained by the gravitational field of 
the earth. 

A world survey covering all continents and oceans 
from the Arctic to the Antarctic [12] showed no sig- 
nificant deviations even comparatively near oil fields 
in the United States. The value obtained was 5.239 
± 0.002 ppm with a standard deviation of ±0.008 
ppm [11]. It is apparent that the turbulence of the 
troposphere quickly eliminates any nonuniformity re- 
sulting from localised He discharge. 

ATMOSPHERIC GASES OF CONSTANT 
PERCENTAGE 

While surveys over large areas have been carried 
out only for the four gases O2, CO2, A, and He, the 
constancy in the total percentage of these gases makes 
it plausible that other gases too must have a constant 
total percentage, unless they are subject to vapour- 
pressure equilibria (as is H2O) or to radiation equilibria 



(as is O3), or are simply the result of some industrial 
activity (as are SO2 and h). 

Nitrogen (A''2). For the analysis of A^2 no direct pre- 
cision method has been discovered. However, as the 
sum of nitrogen and rare gases (called "atmospheric 
nitrogen" by Krogh) has a constant value of 79.0215 
per cent, and as this sum is constant to at least ±0.002 
per cent, A''2 too must be constant to the same degree. 

Neon (Ne). The most reliable data for the Ne content 
of air are (1) a single analysis by Watson [c. 11] who 
found 18.2 ppm, (2) three analyses by Glueckauf [11] 
who found a mean of 18.21 ± 0.04 ppm, and (3) recent 
analyses by Chackett, Paneth, and Wilson [6] who 
found 18.1 ± 0.08 ppm. 

Krypton (Kr) and Xenon (Xe). Of the figures in the 
literature [c. 16], those by Moureu and Lepape and 
by Damkohler appear to be the most reliable.. As 
these values are accurate only to ± 10 per cent of their 
value, the Kr and Xe contents have recently been re- 
determined with a much higher accuracy by the author 
of this article. The figures in parts per million by 
volume are: 

Moureu -|- Lepape (1926) Kr: 1.0 ±0.1, Xe: 0.09 ± 0.01 
Damkohler (1935) Xr; 1.08 ± 0.1, Xe; 0.08 ±0.01 

Glueckauf -f- Kitt (unpub- 
lished) Kr: 1.14 ± 0.01, Xe: 0.087 ± 0.001 

Nitrous Oxide (N^O). The presence of nitrous oxide 
in atmospheric air was discovered by Adel [15, Chap. 
10] by means of an absorption band at 7.8 m in. the 
solar spectrum. Since then further atmospheric ab- 
sorption bands have been discovered at 3.9 fi, 4.5 n, 
and 8.6 m- The recent chemical analysis by Slobod and 
Krogh [20] of N2O in air at ground level gave a value 
of 0.5 ± 0.1 ppm, which is in agreement with the 
spectroscopic data. 

Methane (CHi). Methane was found by spectro- 
scopic identification of its absorption band in sunlight 
modified by the passage through the earth's atmosphere 
over Columbus, Ohio (Migeotte), over Flagstaff, Ari- 
zona (Adel), and over Pontiac, Michigan (McMath 
Observatory) [15, Chap. 10]. From the latter data the 
CHi content of air has been estimated to be about 1.2 
ppm (by weight), that is, about 2.2 X 10~* by volume. 
It is possible that this figau-e is somewhat high, as 
during the process of distillation of air it is found that 
the Kr and Xe fraction contains only an amount of 
CHi roughly equal to that of these gases (1.2 X 10~* 
by volume). 

We are faced with the question of the origin of this 
CHi which is constantly destroyed by the ozone in 
atmospheric air. As a constant source of this CHt we 
may consider either decay of biological products, or 
gas escaping from oil wells, or both. The question of 
the relative extent of these two processes can be decided 
by determining the content of radiocarbon ('""C) in the 
CHi of air. Methane from biological sources contains 
0.95 X 10-12 g of "C per g of C, while mineral CHt 
is inactive. 

At the suggestion of the author, Prof. F. W. Libby 
at the University of Chicago analysed the ''C content of 



COMPOSITION OF THE ATMOSPHERE 



atmospheric methane and found it to coincide with that 
of biological methane. The analysis also places an upper 
limit of about 200 years on the mean hfetime of the 
methane in the atmosphere and suggests an annual 
production of upwards of 10' tons of methane from 
biological sources. 

Hydrogen {H^). The H^ content of air is known 
only approximately. Paneth [16] concludes that it is a 
constant constituent of atmospheric air and that its 
amount can be assumed to be about 5 X 10"'' by vol- 
ume. Recent analyses by the author and G. P. Kitt gave 
varying amounts of Hi upwards of 0.4 ppm, and in- 
vestigations are in progress to see whether these varia- 
tions occur in the free air or are due to local contam- 
ination. 

Summary. The figures believed to be most reliable 
for the constituents of dry air are listed in Table V. 

Table V. Nonvariable Components of Atmospheric Air 



Constituent 


Content (per cent) 


Content (ppm) 


iVa 


78.084 d= 0.004 

20.946 ± 0.002 

0.033 ± 0.001 

0.934 ± 0.001 




O2 




CO2* . 




A 




Ne 


18.18 ± 0.04 


He 


5.24 ± 0.004 


Kr 


1.14 ± 0.01 


Xe 


0.087 ± 0.001 


Hi 


0.5 


CH^ . . 


2 


mo 


0.5 ± 0.1 



* Extrapolated to 1950 according to Fig. 1. 

CONSTITUENTS OF VARIABLE 

CONCENTRATIONS 

(Excluding Water Vapour) 

A rough survey of some of these constituents is 
given in Table VI. 

Table VI. Variable Constituents of Dry 
Atmospheric Air 



Constituent 


Origin 


Proportion in ground air (range) 


O3 


Ultraviolet radia- 
tion 

Industrial 

Industrial 

Biological or oxy- 
dation of CH4 

Industrial 

Sea spray 

Industrial 

Industrial 


fO to 0.07 ppm (summer) 
\0 to 0.02 ppm (winter) 

to 1 ppm 

to 0.02 ppm 

Uncertain 

Up to 10-* g m-3 
Order of 10"* g m-^ 
to trace 


SO2 


NOi 

CH,0 

h. . . . 


NaCl 

NH3 

CO 







Ozone (O3). The bulk of atmospheric O3 is con- 
tained in the stratosphere, where it is produced by the 
ultraviolet radiation from the sun. The problems con- 
nected with its production and occurrence there form 
the subject of a separate article in this Compendium.^ 
We shall deal here only with observations of O3 near 
the surface. 



3. Consult "Ozone in the Atmosphere" by P. W. P. Gotz, 
pp. 275-291. 



Methods of Determination. The main difficulty in the 
determination of O3 in atmospheric air lies in the fact 
that simple chemical reactions are not specific for O3 
and that gases like HiO^, NO2, and SO2 interfere with 
the chemical determination, the first two by increasing, 
the last by decreasing the analytical result. However, 
these gases occur only in the vicinity of human habi- 
tation. On the other hand, the spectroscopic investiga- 
tion of surface air [7, 13], though accurate, is so time- 
consuming (due to the necessary photometry of the 
spectrograms) that it does not lend itself to routine 
observations. This also applies to the chemical method 
of Edgar and Paneth [c. 12] which relies on the separa- 
tion of O3 from all other gases by low-temperature 
adsorption on silica gel. However, two accurate methods 
have been evolved which give reliable results in a 
comparatively short time and thus make possible large 
numbers of determinations under quickly changing me- 
teorological conditions. (See V. H. Regener [c. 17] and 
Glueckauf, Heal, Martin, and Paneth [c. 12].) 

The results obtained so far can generally be explained 
on the basis that O3 which is produced in the higher 
regions — ^mostly in the stratosphere and possibly some 
just below the tropopause — reaches the ground level 
through the turbulence of the air, and on its way down 
is gradually diminished and eventually destroyed by 
oxidisable materials of an organic and inorganic char- 
acter. 

Diurnal Variations. On days with little turbulence, 
the ground O3 found during the day usually disappears 
at nightfall because of the increased stability of the air, 
but it remains unaffected at higher wind velocities. 

Annual Variations. Pronounced maxima (7 X 10~* 
by volume about May) and minima (2 X 10~' about 
November) of the ground O3 have been found by many 
observers. The fact that these annual variations are 
greater than those of the total O3 may be due to the 
greater instability of the atmosphere during the sum- 
mer months. There are some indications that at higher 
latitudes {e.g., Abisko, Lapland) the high summer 
values of ground O3 appear later, if at all. 

Geographic Variations. Next to nothing is known 
about the geographical distribution of O3 over conti- 
nents and oceans. Almost all determinations have been 
carried out between the latitudes 45 °N to 68 °N over 
land. Usher and Rao [22], however, reported the ab- 
sence of ground O3 in India. This result may not be 
reliable, but there is obviously wide scope for further 
investigations. 

Ozone during Depressions. The usually high wind 
velocity and atmospheric turbulence during depressions 
result in high O3 contents (subject to the seasonal 
variations). However, low values of O3 were found 
at Durham, England [10], even at high wind velocities 
in advance of warm fronts, and during occlusions of 
the cold-front type. Apparently under these conditions 
inversions are formed which restrict the turbulent inter- 
change of air masses near the ground with the O3 
produced in higher regions. It is to be expected that 
such phenomena will be greatly reduced in regions 
with low industrial contamination {e.g., over the 



THE COMPOSITION OF ATMOSPHERIC AIR 



oceans), but no experimental data are available to 
check this argument. 

Ozone during Thunderstorms. Dobson [c. 10] has ob- 
served many cases where the total O3 increases during 
thunderstorms and during the passage of thunder- 
clouds. There can be little doubt that these changes 
occur in the tropospheric air and are caused by electric 
phenomena. A continuous measurement [10] during a 
thunderstorm gave no indication of any abnormal in- 
crease of O3 near the ground and on this occasion, at 
least, the Oj-bearing air masses did not reach ground 
level. Other observers [13], however, found abnormally 
high O3 values in ground air on some thundery days. 

Vertical Distribution of Ozone in the Troposphere. An 
increase of the O3 content with height in the troposphere 
is shown by the data of Chalonge, Gotz, and Vassy [7], 
who found an average of 1.7 X 10~* at Lauterbrunnen, 
Switzerland (800 m), and 3.0 X 10"^ at Jungfraujoch, 
Switzerland (3450 m). 



ID 



7- 



AUG 21, 1942 



AUG 24,1942 




12 3 4 

OZONE IN I0"8 PER VOL. 

Fig- 2. — Vertical distribution of ozone in the troposphere. 

(After Ehmert [c. 17].) 

Ozone determinations made in aircraft by Ehmert 
[c. 17] show a variety of features (see Fig. 2). In one 
case the air above cloud level has O3 contents which, 
if measured in volume per volume, are independent of 



height. This would be expected if the mixing ratio is 
kept constant by turbulence. Much less obvious is the 
fact that the O3 content is high in cloudy regions and 
reaches a maximum just below cloud level. Regener 
[17] explains these maxima as produced by advection, 
which may sometimes be the case. However, the re- 
peated occurrence of stratified clouds near such an O3 
maximum seems to indicate that under these conditions 
O3 may be produced by phenomena of an electrical 
nature. 

Sulphur Dioxide (SO2). The quantities of SO2 found 
in air vary greatly according to the nearness of towns 
and the turbulence of the air. To give a few examples: 
An average of 0.033 ppm was found at the Boyce 
Thompson Institute (about 15 miles from New York 
City) ; at Chicago an average of from 0.06 to 0.27 ppm 
was found in residential districts and from 0.4 to 0.5 
ppm in manufacturing districts. In the presence of O3, 
air may be expected to be free of Sd. 

Nitrogen Dioxide {NO2). No systematic determina- 
tions of this constituent seem to have been made. This 
is largely because of the small quantity present in air 
and the difficulty of analysis. A very reliable method 
of NO2 analysis in air, based on the use of 2:4 xylen- 
l-ol was used by Edgar and Paneth [c. 12]. From the 
fact that on a large number of days the NO2 content 
found in this way was below the threshold of sensitivity 
(5 X 10~"), one is tempted to conclude that NO2 is 
not a normal constituent of air. This may be due essen- 
tially to its high solubility in water. In large to^^ms, 
however, where NO2 occurs as a by-product from the 
combustion of nitrogenous matter, varying quantities 
up to 2 X 10~* were found by a number of authors. 

Ammonia {NH{). The presence of minute amounts 
of NH3 in atmospheric air over Michigan has been 
claimed by Mohler, Goldberg, and McMath [c. 15, 
Chap. 10] from absorption bands in the 2-;u region. 
But, as Migeotte and Chapman [c. 15, Chap. 10] have 
pointed out, the 10.5-/X fundamental band of NH3 is 
much more suitable for testing the presence of atmos- 
pheric NHi, and no evidence could be found in this 
region of absorption either above Flagstaff, Arizona, 
or above Columbus, Ohio. Moreover, NH3 is very 
soluble in water and thus is not likely to be retained 
in the air for any lengthy period. 

Carbon Monoxide (CO). This gas was observed spec- 
troscopically by Migeotte [c. 1] over Columbus, Ohio, 
as well as on the Jungfraujoch (3580 m altitude) but, 
as none could be found by Adel over Flagstaff, Ari- 
zona [1], it is not yet certain whether it is a permanent 
constituent of the atmosphere. 

THE UPPER ATMOSPHERE 

The composition of air in the upper atmosphere is of 
considerable interest as an indicator of whether or not 
large-scale mixing of air masses takes place in the 
stratosphere. It is often assumed that the absence of a 
systematic temperature gradient in the stratosphere is 
incompatible with large-scale mixing. In the absence 
of turbulent mixing, however, diffusive separation of 
the gases should take place and the lighter gases should 



8 



COMPOSITION OF THE ATMOSPHERE 



become relatively more abundant with increasing 
height. 

The most direct method of finding the level where 
diffusive separation begins is the chemical analysis of 
air samples taken at great heights, since the gravita- 
tional equilibrium should cause the O2 content to de- 
crease by 2 per cent per kilometre and the He content 
to increase by 14 per cent per kilometre. Air samples 
from the stratosphere have been obtained by manned 
and unmanned balloon flights. The results of these 
analyses are shown in Table VII. 

Table VII. Composition of Air in the Stratosphere 



Height 
(km) 


Helium variation 
(per cent) 


Oxygen variation 
(per cent) 


Source of data* 


9-17 







C 


14.5 




-0.14 


d 


16.5 


-1-0.5 ± 0.5 




e 


18.0 


-1-0.35 ± 0.1 




e 


18.6 


-1-0.7 ± 0.3 





e,a 


18.5 




-0.38 


d 


19.0 


-t-0.55 ± 0.15 


-0.24 


e,d 


21.0 


4-6.9 ± 0.7 




e 


21.5 




-0.24 


b 


22.0 


-1-4.1 ± 0.2 




e 


22.0 


-t-1.95 ± 0.15 




e 


22.5 


-1-5.1 ± 0.6 




e 


22.5 


-M.9 ± 0.3 




e 


23.5 


-t-4.0 ± 0.3 




e 


23.5 


-fO.3 ± 0.15 




e 


24 




-0.86 


d 


25 


-1-2.1 ± 0.3 




e 


28-29 




-2.5 


d 



* Manned balloon flights Unmanned balloon flights 

(a) Prokofiev, 1933 (c) Lepape and Colange, 1935 

(6) Explorer II, 1936 (d) E. Regener, 1936 

(e) Glueckauf and Paneth, 1946 

It appears from this table that there is no significant 
change in either the He content or the O2 content below 
20 km. The He surplus observed between 21 and 25 
km averages 3.3 per cent, an enrichment which should 
be found at the top of a column of still air only 250 m 
high. The biggest O2 deficit, at about 28 km, corre- 
sponds to a column of still air only 1100 m high. It is 
therefore apparent that at the heights reached by 
sounding balloons there is sufficient turbulence to reduce 
the changes in the He content to about }io of what 
one would expect from a gravitational equilibrium start- 
ing at the tropopause. The recent analysis by Chackett, 
Paneth, and Wilson [6] of three air samples collected 
by a V-2 rocket from a height of 50 to 70 km, gave 
variations of -|-0.3 to —4 per cent for He, variations of 
— 0.3 to —0.7 per cent for Ne, and variations of —0.4 
to -f 1.0 per cent for A. These results make it certain 
that no diffusive separation is maintained even at these 
great heights. 

ISOTOPIC COMPOSITION OF THE 
ATMOSPHERIC GASES 

Increased attention to the isotopic composition of 
the atmospheric gases is likely to throw light on a 
number of problems. The composition in most cases is 



very similar to that found in the same atomic species 
in other parts of the earth's crust^ (see Table VIII). 

Water Vapour. Because of differences in the vapour 
pressures, mainly of Wz^O, Wa'^O, and WWi^O, the 
density of atmospheric water should be slightly less 
than that in the oceans from which it originates. This 
was confirmed by Riesenfeld and Chang [19] who found 
a deficit of 3.8 7 in the density of snow water, and of 
2.5 7 for rain water (17= 10~^ g ml-^. These figures 
are approximately what would be expected from the 
known vapour pressures. 

Oxygen. The differences in the composition of the 
oxygen in (liquid) water, gaseous oxygen, and carbon 
dioxide are much smaller, the densities being in the 
ratio 1:1.0000073:1.0000116 [23]. From this follows a 
slight enrichment of the ^^0 isotope in the ratio 
1:1.0033:1.0053. The difference of the oxygen density 



Table VIII. Isotopic Composition of the Main 




Atmospheric Gases 




Atomic mass numbers (in parentheses) and percentages 




(in italics) of isotopic species 


HinffjO 


(1) 99.98 (2) 0.02 


He 


(3) 1.1 X 10-^ (4) 100 


C in CO2 


(12)98.9 (13) 1.1 (14) 0.95X10-'-^ 


N 


(14) 99.62 (15) 0.38 





(16) 99.757 (17) 0.039 (18) 0.20^. 


Ne 


(20) 90.00 (21) 0.27 (22) 9.73 


A 


(36) 0.307 (38) 0.061 (40) 99.632 j^B 



for atmospheric CO2 and for that of carbonate rocks 
is negligible [9]. 

Hydrogen. The difference in the isotopic composition 
between atmospheric H^ and water vapour in air has 
not been determined, but if the two are in equilibrium 
(which is not necessarily the case), one would expect 
a considerably reduced deuterium-hydrogen ratio in the 

gaseous hydrogen, as ^^^^m *'' "'"""' = ^.6 (Suess [21]). 

(-L'/-n) hydrogen 

Helium.^ Much greater differences are observed for 
the We content of helium found in air, in rocks, and 
in oil wells (Aldrich and Nier [2], and Coon [8]), the 
ratios mej^He being 1.2 X 10"^, 1.5 X 10"', and 
3 X 10~^, respectively. This clearly points to a differ- 
ent mode of origin of the two He species in the three 
cases. The We in the atmosphere is suspected to arise 
from the reaction of nitrogen with neutrons derived 
from cosmic radiation. The We in the lithosphere is 
presumably due to the action of neutrons on Li whei-e 
the neutrons arise from known reactions of small atomic 
nuclei with the a particles of the natural radio-ele- 



4. The questions of the origin and development of the at- 
mosphere, though of interest to meteorologists, cannot be 
adequately dealt with in this paper. Attention is drawn to 
detailed articles by Chamberlin, Brown, and Kuiper [15, 
Chaps. 8, 9, 12], and by Wildt [24] where further references 
may be found. 

5. (Added in press) See also the recent note by P. Harteck 
and V. Faul tings on "The ^He-Problem of the Atmosphere."- 
Nature, 166:1109 (1950). 



THE COMPOSITION OF ATMOSPHERIC AIR 



9 



ments. The connection of We in minerals with Li is 
borne out by the abnormally high ^He/*He ratio in 
spodumene, a lithium aluminium silicate. 

Carbon. Another isotope which owes its existence to 
the neutrons from cosmic radiation is the radioactive 
i^C, which is produced by ^W + n ^ W + '^C. 

As cosmic ray neutrons are produced mainly in the 
upper atmosphere, the "C starts its career as CO2 and 
enters into all organic matter by the process of plant 
assimilation. After the death of the plant the radio- 
active carbon decays with a half-life of 5720 years, so 
that old coal and oil deposits are no longer radioactive. 
The proportion of radiocarbon was found to be 0.95 
X 10-1- g of "C per g i^C in living matter [3]. 

FUTURE DEVELOPMENTS 

Oxygen and Carbon Dioxide. Our best values of the 
O2 content or, for that matter, of the O2 and CO2 
content of air date from 1912. Since then a number of 
improvements in the control of thermostats and in all 
manner of measuring devices have been made, which 
should render possible an increased accuracy. A re- 
determination is particularly desirable in order to get 
an idea of any long-term variations of the O2 content 
of air. 

There are, moreover, the unexplained O2 values of 
Lockhart and Court in the Antarctic which should be 
either confirmed or refuted. This applies also to the 
high CO2 values observed by Krogh in certain arctic 
regions, where the observed variations were very large, 
and further investigations are likely to bring to light 
some interesting phenomena responsible for such 
changes. Callendar's suggestion of a CO2 increase during 
this century due to industrial CO2 production requires 
that the CO2 content of the Northern Hemisphere should 
be slightly larger than that of the Southern Hemi- 
sphere, a feature which should be subject to experimen- 
tal verification by modern techniques. 

The results of Buch and of Wattenberg make it 
fairly certain that there is a CO1 circulation in the oceans 
involving uptake of CO2 at high latitudes and its re- 
lease at low latitudes. Some light on the time scale of 
this cycle might be thrown by a '^C analysis of the 
CO2 released from the sea at low latitudes, which, if 
the cycle exceeds 10' years, would result in a noticeable 
decrease of ^*C activity. 

Methane. The CHi in the atmosphere, discovered 
only recently, still offers a few problems. Its percentage 
in air requires more accurate determination, and the 
question of its production requires further study. 

Hydrogen. Our knowledge of the H2 content of the 
air is so far inadequate. 

Ozone. Large gaps still exist in our knowledge of the 
atmospheric O3 near the ground. Its geographical dis- 
tribution at ground level is quite unexplored; its de- 
pendence on weather conditions has only been touched 
on, and requires much more systematic investigation, 
particularly with reference to its vertical distribution. 
The increased occurrence of O3 near cloud levels and 
its connection with thunder clouds also require more 



detailed investigation, including a study of its possible 
mode of generation under such conditions. 

Upper Atmosphere. It now seems certain that the 
upper atmosphere has essentially the same composition 
as that found at the ground, at least up to heights of 
70 km, though further confirmation of the rocket data 
is desirable and will no doubt be obtained in the near 
future. This uniformity means that turbulent mixing 
in the stratosphere is considerably greater than was 
formerly expected. An explanation for this turbulence 
has been suggested by Brewer [4] who assumes an air 
circulation involving a movement of air into the strato- 
sphere at the equator followed by slow poleward move- 
ment in the stratosphere, accompanied by a slow sinking 
movement in the temperate and polar regions. As this 
hypothesis requires the abandonment of the idea of a 
stratosphere which is in radiative equilibrium, many 
new and interesting problems arise which require ex- 
perimental confirmation. 



REFERENCES 



1. Adel, a., "Concerning the Abundance of Atmospheric 

Carbon Monoxide." Phys. Rev., 75:1766-1767 (1949). 

2. Aldbich, L. T., and Nier, A. C, "The Occurrence of 

3He in Natural Sources of Helium." Phys. Rev., 74:1590- 
1594 (1948). 

3. Andeeson, E. C, and others, "Natural Radiocarbon from 

Cosmic Radiation." Phys. Rev., 72:931-936 (1947). 

4. Brewer, A. W., "Evidence for a World Circulation Pro- 

vided by the Measurements of Helium and Water Vapour 
Distribution in the Stratosphere." Quart. J. R. meteor. 
Soc, 75:351-363 (1949). 

5. Callendar, G. S., "Variations of the Amount of Carbon 

Dioxide in Different Air Currents." Quart. J. R. meteor. 
Soc, 66:395-400 (1940). 

6. Chackett, K. F., Paneth, F. A., and Wilson, E. J., 

"Chemical Analysis of Stratosphere Samples from 50 
to 70 Km. Height." J. atmos. ierr. Phys., 1:49-55 (1950). 

7. Chalonge, D., Gotz, F. W. P., et Vassy, E., "Mesures 

simultan^es de la teneur en ozone des basses couches de 
I'atmosphere a Jungfraujoch et k Lauterbrunnen." 
C. R. Acad. Set., Paris, 198:1442 (1934). 

8. Coon, J. H., "Isotopic Abundance of 'He." Phys. Rev., 

75:1355-1357 (1949). 
Dole, M., and Slobod, R. L., "Isotopic Composition of 

O.xygen in Carbonate Rocks and Iron Oxide Ores." 

J. Amer. chem. Soc., 62:471-479 (1940). 
Glueckauf, B., "The Ozone Content of Surface Air and 

Its Relation to Some Meteorological Conditions." Quart. 

J. R. meteor. Soc, 70:13-19 (1944). 

— "A Micro-analysis of the Helium and Neon Contents 
of Air." Proc roy. Soc, (A) 185:98-119 (1946). 

— and Paneth, F. A., "The Helium Content of Atmos- 
pheric Air." Proc. roy. Soc, (A) 185:89-98 (1946). 

13. Gotz, F. W. P., Schein, M., und Stoll, B., "Messungen 

des bodennahen Ozons in Zurich." Beitr. Geophys., 

45:237-242 (1935). 
Krogh, A., "Abnormal Carbon Dioxide Percentage in the 

Air in Greenland. . . ." Medd. Grt^nland, 26:407-435 

(1904). 
Kuiper, G. P., ed.. Atmospheres of the Earth and Planets. 

Chicago, University of Chicago Press, 1949. (See Chaps. 

8, 9, 10, and 12.) 



9. 



10 



11. 



12 



14 



15 



10 



COMPOSITION OF THE ATMOSPHERE 



16. Paneth, F. a., "The Chemical Composition of the Atmos- 

phere." Quart. J. R. meteor. Soc, 63:433-438 (1937). 

17. Regenbr, E., "Ozonschieht und atmospharisohe Turbu- 

lenz." Meteor. Z., 60:235-269 (1943). 

18. Regnault, M. v., "Recherches sur la composition de Pair 

atmosph^rique." Ann. Chim. (Phys.), 3* s^r., 36:385- 
405 (1852). 

19. RiBSENFELD, E. H., und Chang, T. L., "Die Verteilung 

der schweren Wasser Isotope auf der Erde." Natur- 
wissenschaflen, 24:616-618 (1936). 

20. Slobod, R. J., and Kbogh, M. E., "Nitrous Oxide as a 

Constituent of the Atmosphere." /. Amer. chem. Soc, 
72: 1175-1177 (1950). 



21. SuEss, H., "Isotopen Austauch Gleichgewichte" in FIAT 

Rev. of German Sci., 1939-1946, Vol. 30, Physical Chemis- 
try, pp. 19-24. Off. Milit. Govt. Germany, Field Inform. 
Agencies, Tech. Wiesbaden, 1948. 

22. Usher, F. L., and Rao, B. S., "The Determination of 

Ozone and Oxides of Nitrogen in the Atmosphere." 
/. chem. Soc, 111:799-809 (1917). 

23. Vinogradow, A. P., and Teis, R. V., "Isotopic Composi- 

tion of Oxygen of Different Origins." C. R. (Doklady) 
Acad. Sci. URSS, 33:490-493 (1941). 

24. WiLDT, R., "The Geochemistry of the Atmosphere and the 

Constitution of the Terrestrial Planets." Rev. mod. 
Phys., 14:151-159 (1942). 



RADIATION 

Solar Radiant Energy and Its Modification by the Earth and 

Its Atmosphere by Sigmund Fritz 13 

Long- Wave Radiation by Fritz Moller 34 

o 

Actinometric Measurements by Anders Angstrom 50 



SOLAR RADIANT ENERGY AND ITS MODIFICATION BY THE EARTH 

AND ITS ATMOSPHERE 

By SIGMUND FRITZ 
U. S. Weather Bureau, Washington, D. C. 



The sun is the principal source of the energy which, 
by devious means, becomes the internal, potential, and 
kinetic energy of the atmosphere. The solar irradiation 
of a unit horizontal surface at the outer limits of the 
earth's atmosphere can be evaluated, at least in relative 
units, from astronomical and trigonometrical considera- 
tions [61]; thus on a relative scale, the diurnal and 
seasonal variations of this solar irradiation above the 
atmosphere are known. On the average, variations simi- 
lar to these occur also at the earth's surface, and the 
associated diurnal and seasonal changes in atmospheric 
temperature are commonplace knowledge [52]. 

There are, however, additional changes in effective 
solar irradiation of the planet Earth which are super- 
posed on the trigonometrical variations. These are of 
two kinds. The first is due to the change in the quality 
and quantity of energy which leaves the sun. The second 
is caused by changes in the reflectivity of the atmo- 
sphere (including clouds) and of the earth's surface; the 
solar energy which is immediately reflected to space 
cannot be meteorologically effective. 

In contrast to the regular, astronomically induced 
changes in meteorological parameters (notably diurnal 
and seasonal atmospheric temperature changes), the 
large-scale meteorological consequences of these irregu- 
lar changes in solar irradiation are far from obvious, 
if, indeed, any such meteorological effects can be shown 
to be induced at all by them. For example, changes of 
the first kind {i.e., in solar output) have been invoked 
as possible causes of abnormal heating in the ozone 
layer with subsequent pressure changes at the earth's 
surface [44]; changes of the second kind {i.e., in reflec- 
tion by the earth or clouds) are important, for instance, 
in local turbulence of the air near the ground, but are 
rarely used to explain widespread meteorological phe- 
nomena. These as well as other solar-induced meteor- 
ological phenomena are discussed elsewhere in this 
Compendium. In this article we shall, for the most part, 
examine the solar energy itself and shall mention its 
meteorological effects only incidentally. 

SOLAR RADIATION OUTSIDE THE EARTH'S 
ATMOSPHERE 

The Sun. The sun, located about 93,000,000 miles 
from the earth, is a large, hot, gaseous mass. When 
viewed through a smoked glass it appears as a smooth 
circular disk which is called the -photosphere, but when 
examined with the aid of more refined techniques, the 
photospheric surface appears highly granulated and is 
surrounded by a gaseous envelope which is commonly 
divided into three layers for descriptive purposes. Of 
these the one just outside the photosphere is the rela- 



tively thin reversing layer, so called because the spectral 
lines ordinarily seen as dark absorption lines in the 
photospheric spectrum appear as bright emission lines 
when examined in the reversing layer; still farther from 
the photosphere is the chromosphere; and beyond that 
is the corona [4]. The sun's "surface" and its surroimd- 
ing atmosphere are by no means static. The presence 
of short-lived photospheric grains, dark sunspots, bright 
areas (faculae and flocculi), and erupting prominences 
indicate that the entire observable sim is in a state of 
considerable turmoil. This turmoil is associated with 
variations in the quantity and spectral intensity dis- 
tribution of the solar energy which subsequently irra- 
diates the outer limits of the earth's atmosphere. 

Average Spectral Distribution of Sunlight. To calcu- 
late the solar energy available for meteorological proc- 
esses, it is desirable to measure the amount of solar 
energy Jo (the so-called solar constant) which reaches 
the outer atmosphere of the earth. To determine the 
interaction between our atmosphere and the sxm's 
energy, the distribution of spectral intensity lox of the 
extraterrestrial solar energy is also required. For both 
of these quantities we are largely indebted to the Astro- 
physical Observatory of the Smithsonian Institution, 
whose determinations of Jo and /ox are monuments to 
the work of the Observatory. 

Until recently, the sun's energy had not been directly 
observed below wave lengths of about 2900 A because 
of the absorption of energy of shorter wave lengths by 
the envelope of ozone which surrounds the earth up to 
about 50 km. For wave lengths greater than 2900 A, 
selective scattering and absorption, mainly by air, dust, 
and water vapor, modify the solar spectrum; these 
troublesome modifications must be eliminated from 
measurements made at the ground under cloudless skies 
to obtain the extraterrestrial spectrum. In the region 
from about 0.29 ix to 2.5 m numerous measurements and 
extrapolations have been made. The Smithsonian Insti- 
tution [3] is the main source of spectral information for 
the region above 3400 A, but its latest smnmary of data 
was compiled in 1923 [2]. Recently, V-2 rocket observa- 
tions have ex-tended the measured spectrum down to 
2200 A [47]. 

Visible and Near Infrared Radiation. Both the total 
amount and the spectral distribution of the radiant 
energy emitted by a black body are detennined by its 
temperature. It is therefore convenient to describe the 
radiant energy from a source in terms of the black-body 
temperature which would most nearly produce the ob- 
served energy. The sun does not radiate as a black 
body. Despite this fact, the average observed energy 
curve from about 0.45 m to about 2.0 ju closely approxi- 



13 



14 



RADIATION 



mates the spectral-energy distribution of a black body 
(Fig. 1). It is therefore not unusual to speak of the 
black-body temperatiu-e of the sun as 6000K, although 
this numerical value may vary by several hundred 
degrees depending upon the method used to calculate 
it [4]. For example, the total energy emitted by a black 
body per unit area per imit time is given by aT^, where 
T is its temperature in degrees absolute and o- is the 
Stefan-Boltzmann constant. The solar constant is com- 
monly taken as 1.94 ly min"' (where ly = langley = 
g cal cm^^), and considering the distance from the 
earth to the sun, we can calculate the total energy 
emitted by the sun. Then, by introducing the sun's 



700 
500 

300 

>:2oo 

ID 

z 
I- 
- 100 

(Ij 

> 70 

I- 
< 

^ 50 
cr 

30 
20 



10 




V FABRY a BUIS50N 
*PETT1T 
• WILSING 
A 1903-1910 
^ I903-I9I0(0MITTING QUARTZ RESULTS 1 
□ 1916-1918 
'O -- O 1920-1922 

SLACK BODY 6000 K 

PROPOSED STANDARD CURVE 



0.3 



0.4 0.5 0.7 1.0 1.5 
WAVELENGTH (MICRONS) 



2.0 



3.0 



Fig. 1. — Spectral intensity distribution of solar radiation 
outside the eartli's atmosphere. {After Moon [63].) 

area, we calculate the energy radiated per square centi- 
meter of solar surface. Placing that energy equal to cT*, 
we get T = 5770K. 

Another temperature estimate results from Wien's 
displacement law for black bodies: Xmax T = const, 
where Xmax is the wave length of maximiun intensity. 
Abetti [4] takes X„,ax = 4740 A and finds T = 6080K. 

It should be emphasized that at wave lengths out- 
side the region 0.45 n to 2.0 n solar energy departs 
markedly from that of a black body at 6000K. Moon 
[63] has combined the results of several authors and ob- 
tained Fig. 1, which shows the relative intensity Jox 
of the energy as a function of wave length. 

Ultraviolet Radiation. The energy in the ultraviolet 
spectrum is well below that of a black body at 6000K; 
this has been established by several investigators [35, 
37, 72]. Hulburt's curve [47] in Fig. 2 contains the 
Naval Research Laboratory rocket measurement at 55 



km in which no ozone could be detected and was one 
of a series of spectra observed at levels up to 88 km. 
Other measurements from rockets up to 155 km [20] 
show results similar to those at 55 km and indicate that 
the energy is less than that of a black body at 6000K. 

A recent curve by Gotz and Schoimiann [35], based 
on five observations in the region from 3300 A to 5000 
A, lies far below (by a factor of 2 or more at 3400 A) 
Moon's curve of Fig. 1 ; this is also true of Hess's data 
[55, p. 324]. Perhaps these lower values are due to the 
fact that the Smithsonian observations were troubled 
by scattered hght at short wave lengths. If the rocket 
data (Fig. 2) had been joined to the data of Gotz and 
Schonmann, the resultant spectral curve would ob- 



200 



100 



50 



>- 
I- 



UJ 

^ 20 



> 



UJ 



10 



1 




1 


1 1 


-— 


- 




^eoSi^ 




^ 


'^ I 


~ ^y""^ 


^^ 


/^-\ 


f( 




~ 


SUNLIGHT/ 


f ^ 


^ 1 

1 

1 
f 








u 


J l\IVI / 




1 
1 




- 


- 




y 




/sunlight 

/ 35 K"^' 


- 


f 






/ 

/ 
/ 




- 


i 


1 


1 


/ 

1 


1 





2200 2400 2600 2800 3000 3200 3400 
WAVELENGTH (ANGSTROMS) 
Fig. 2. — Spectral intensity distribution of ultraviolet solar 
radiation measured from a rocket. (After Hulburt [47].) 

viously have been much farther below the 6000K curve. 
Future measurements will decide the true state of af- 
fairs. 

Infrared Radiation. The near infrared has been ob- 
served many times by the Smithsonian Institution. 
Abbot and others [2] considered their 1920-22 curve as 
the best estimate. Their data exceed the black-body 
curve (Fig. 1) in the region near 2 n, but Moon, also 
accepting the earlier data, adopted the 6000K black- 
body curve as the true one beyond 1.25 fi. Beyond 2.5 fi, 
Adel [5] has observed the spectrum up to about 24 /i. 
He finds that the solar temperature is about 7000K in 
the far infrared. 

Short-Wave Radio Radiation. Measurements up to 
24 n have been made by optical means. Recently the 
observations have been extended by radio detection 
instruments into wave lengths of the order of a few 
centimeters to a few meters [39, 62]. These observations 
indicate black-body temperatures of the order of lO^K 



SOLAR RADIANT ENERGY 



15 



or more. It should be pointed out, however, that the 
black-body energy is so small at those wave lengths — 
even during disturbed sun conditions — that radiation 
from a black body at lO^K can contribute only a very 
small amount of thermal energy by comparison with 
the principal solar energy [39]. 

The Unmeasured Radiation. We tiu-n now to an im- 
portant region of unmeasured radiation, namely, the 
ultraviolet energy below 2200 A. 

From a consideration of the ionized states of certain 
elements observed in the sun and from the considera- 
tion of the state of ionization of the earth's ionosphere, 
several investigators have concluded that in the region 
below 1000 A the sun radiates energy corresponding to 
temperatures above 6000K. Greenstein [37] mentions 
the uncertainty regarding the need for assimiing such 
excess ultraviolet radiation and concludes that at least 
for X > 1215 A the temperature corresponding to solar 
energy is probably less than 6000K and is near 5000K. 
For X ^ 900 A he discusses a suggestion by Kiepen- 
heuer and Waldmeir that corona temperatures of lO^K 
enhance the photospheric radiation by a factor of 2 at 
900 A and by 2 X lO'' at 600 A. For X > 900 A no ap- 
preciable radiation is contributed by the corona. Super- 
posed on the average radiations, measured and un- 
measured, are the radiations from the "cool," dark 
sunspots (temperature about 4800K [4]), and the in- 
creased radiation from the bright areas, that is, from 
faculae and flocculi. 

In addition to the electromagnetic radiation de- 
scribed above, the sun also emits particles which are 
responsible for such effects as the aurorae and some 
types of magnetic and ionospheric storms. 

Summary. It appears then that in the optically 
measured spectnma, from about 0.45 ju to 24 /i the sim 
radiates as a black body whose temperature is close to 
6000K, perhaps increasing to 7000K towards the higher 
wave lengths. For shorter wave lengths, at least down 
to 0.22 IX, the measured radiation corresponds to a con- 
siderably lower temperature of about 4000K to 5000K. 
For 1000 A < X <2200 A this lower temperature may 
also apply [37]. But for X < 1000 A the hot corona may 
dominate, resulting in much higher effective black- 
body radiation. In the comparatively long wave lengths 
from 1 cm to 30 m, high temperatures (lO^K) are again 
indicated. In the region from 24 /u to 1 cm, no measure- 
ments seem to have been made. 

Fluctuations of Emitted Radiation. The bright and 
dark markings and other manifestations of changes on 
the sun can be expected to produce spectral emissions 
which differ from the average solar emission. These 
spectral variations are indeed observed directly or in- 
directly in nearly all parts of the solar spectrum. 

Far Ultraviolet. That there are marked changes in the 
far ultraviolet emission from the sun is evident from 
measurements of the reflection of radio waves by the 
ionospheric layers in the earth's upper atmosphere. 
These layers are regions where solar ultraviolet energy 
(X < 1000 A) has ionized the atmospheric gases, with 
the result that they have the property of reflecting 



radio waves of certain frequencies. The approximate 
heights [38, 62] and pressures of those layers are given 
in Table I. 

Table I. Approximate Heights and Pressures of Ionized 

Layers 



Layer 


Height 
(km) 


Approximate pressure 
(mb) 


Fa 

E 
D 


300 

200 

100 

80 to 50 


5 X 10-' 

1 X 10-' 

5 X 10-3 

5 X 10-2 to 1 



The highest frequency radio signal which can be re- 
flected is called the critical frequency jo for the reflecting 
layer, and it can be shown that under certain assump- 
tions [64, p. 59] 



fi - Ni, 



and that 



N\ 



'ox, 



(1) 



(2) 



where Ni is the maximmn ion density of an ionized 
layer. Hence on combining equations (1) and (2), 



fo. 



(3) 



The critical frequency foF^ of the F2-layer fluctuates 
considerably from day to day. When the measured 
daily value of /ofj at noon is plotted against the daUy 
simspot number, no significant correlation can be found 
[69]; on a monthly basis a small correlation may be 
present [13]. However, if a twelve-month running aver- 
age of noon f„F2 is plotted against the twelve-month 
running averages of sunspot nuinbers, a linear relation 
results with very little scatter of the points [64], and 
/oFs increases by a factor of about 2 from simspot 
minimum to sunspot maximum. Similar results appear 
for the Fi- and E-layers; but for these latter layers, fo 
increases by a factor of about 1.2 from sunspot mini- 
mum to sunspot maximxun [9]. The D-region variation 
is apparently similar to the E and Fi variation [64]. 

If equation (3) is applied to the smoothed data over 
the sunspot cycle, 7ox (which may be in a different wave- 
length region for each layer) increases by a factor of 
approximately 2 for the E- and Fi-regions [9, 64]. But 
since /0F2 increases by a factor of 2, /ox would increase 
sixteenfold in the Fo-region [64]. However, other rela- 
tions have been mentioned for the Fa-layer. Mitra [62] 
indicates that instead of equation (2), Ni «: 7ox applies 
here; this leads to 7ox <^ fl. Allen [9] prefers 7ox <^ /<,. 
Mitra 's relation leads to a fourfold increase in 7o\, while 
Allen's relation leads to a twofold increase. We may 
conclude therefore that 7ox, which produces the F2- 
layer, surely increases from sunspot minimum to sun- 
spot maximum and that the amount of the increase is 
at least twofold. 

What is the significance of ionospheric heating for 
tropospheric meteorology? Since very little direct rela- 
tion exists between the critical frequencies and the 
unsmoothed sunspot data, some effect (possibly solar) 



16 



RADIATION 



other than sunspots must produce these ionospheric 
variations; only on the average is the ultraviolet in- 
tensity correlated with sunspots. We should expect 
therefore that the meteorology of the troposphere would 
not be correlated with sunspots on a daily basis if 
ionospheric variations were used as a criterion. What 
about longer periods? The wave lengths involved are 
of the order of 1000 A or less, so that the amount of 
energy is small and the pressure (about 10"^ mb or less) 
and density of the absorbing layers are so small that it 
seems unlikely that heating in the ionosphere by the 
increased ultraviolet energy can directly affect the me- 
teorology of the lower atmosphere; at least that is the 
view of one school of thought [71, p. 504]. Therefore 
for longer periods also, if only the ionosphere were in- 
volved in variable ultraviolet absorption, no tropo- 
spheric effect would be noticed. 

At present, one cannot specify the height at which 
anomalous heating in the upper atmosphere can affect 
the troposphere through dynamic processes. However, 
if in addition to an increase in the radiation which heats 
the ionosphere, increases also occur in the ultraviolet 
energy which can penetrate to lower layers, for example, 
to the top of the ozone region (40-50 km) where the 
pressiu-e is of the order of 1 to 3 mb, then dynamic 
pressure changes caused by additional heating are more 
likely [44; 71, p. 504]. And indeed such ultraviolet 
energy increases may occur, but it is not certain at 
present that significant increases occur at wave lengths 
which can heat the ozonosphere. 

There are several solar-induced effects in the iono- 
sphere, as revealed by magnetic and radio data, and 
from the ozone-heating viewpoint at least one of these 
ionospheric phenomena deserves further mention. That 
phenomenon is the radio fade-out or sudden ionospheric 
disturbance (SID). SID's are caused Avhen radio waves 
transmitted upward from the ground are strongly ab- 
sorbed in the D-layer, so that they cannot be reflected 
back to the ground by the higher ionospheric layers. 
The increased absorption of the radio waves is caused 
by a sudden increase in the ionization of the D-layer; 
the increased D-layer ionization is caused by a sudden 
large increase in the solar ultraviolet energy which 
reaches and is absorbed by the layer. In short, SID's 
are caused by sudden increases in ultraviolet solar 
radiation and occur simidtaneously with the appear- 
ance of visible bright solar flares on the sun (chromo- 
spheric eruptions). 

Moreover, it is found that during SID's the F-layers 
are practically unaffected and the E-layer is only 
slightly affected. Hence the upper ionospheric regions 
are apparently transparent to the ionizing radiations 
in this case, while the lower D-region absorbs them 
strongly. The duration of SID's is of the order of a few 
minutes to a few hours, and their intensity is of course 
variable. 

Here then is a phenomenon which produces short- 
lived intense ionization, and hence heating in the vicin- 
ity of 60 km. Since the upper layers are unaffected, the 
radiation must be of wave lengths such that the air 
above 80 km is transparent. Wulf and Deming [79] 



offer an interesting explanation of this ionization. Ozone 
absorbs very strongly in the region 2300 A to 2800 A, 
but this spectral region is transmitted readily by the 
atmosphere above 60 km. They suggest that partial ab- 
sorption at the top of the ozone layer ionizes the ozone 
there. Increased solar emission at those wave lengths 
may therefore be responsible for the increased D-region 
ionization and hence for SID's. It should be pointed 
out however that the recent V-2 rocket measurements 
[47] could not detect any ozone above 55 km. Probably 
an amount of ozone smaller than could be detected by 
the rocket exists above 55 km and this is sufficient to 
produce the observed ionization.^ 

According to some writers, the increased emission 
during solar flares is contributed largely by specific ele- 
ments, hydrogen and calciimi, for example [25], al- 
though emissions from other elements have been meas- 
ured. Hydrogen does not radiate in the wave lengths 
2300-2800 A. Calcium and some of the other elements, 
on the other hand, do emit monochromatic radiation 
there, so that some increase in /ox occurs during solar 
flares in this region — how much of an increase is still 
unknown. 

Mitra [62] discusses some other SID explanations and 
prefers 973 A as the wave length of the ionizing radia- 
tion. Heating by such radiation in a narrow spectral 
band may be small and should not extend very far into 
the ozonosphere. But if, as Wulf and Deming suggest, 
increased radiant energy in the broad band 2300-2800 
A is emitted, then the resulting increased heating, not 
only at and above 60 km but also lower in the ozono- 
sphere, may have important implications for tropo- 
spheric meteorology [44]. It would therefore be highly 
desirable to measure the distribution of spectral in- 
tensity in this region at frequent intervals. Hulburt [47] 
reports that the solar spectrum near 2200 A was de- 
tected at 34 km from the V-2 rocket, and Brasefield [16] 
has described some temperature measurements from an 
unmanned balloon up to 140,000 ft (42 km). If such 
balloons could be equipped for constant-level ffights at 
40 km or higher and designed to carry spectral measur- 
ing equipment, it would be possible to determine the 
solar spectrum near 2200 A and for X > 2700 A at 
frequent intervals during days of both disturbed and 
undisturbed solar conditions. Such measurements may 
determine whether current ideas regarding solar con- 
trol of weather through heating of ozone have any basis. 

Near Ultraviolet. In a series of optical measurements 
during the years 1924-32, Pettit [68] determined the 
intensity at 3200 A relative to the intensity at 5000 A 
and extrapolated in the usual manner to the "top" of 
the atmosphere. Presumably the intensity at 5000 A 
changed rather little, so that the variation in the ratio 
reflects the time variation in the intensity at 3200 A. 
His averaged data show a rather good agreement with 
the smoothed sunspot numbers, low sunspot numbers 



1. At the January 1950 meeting of the American Mete- 
orological Society in St. Louis, Missouri, R. Tousey of the 
Naval Research Laboratory reported a rocket measurement of 
small amounts of ozone up to 70 km. 



SOLAR RADIANT ENERGY 



17 



corresponding to low ultraviolet radiation, as in the 
ionosphere, but at times the correlation was negative 
(June 1928 to June 1929). Since the intensity at sun- 
spot maximum was about 1.5 times that at sunspot 
minimum, he felt that in general the range of the ob- 
served variations at 3200 A was too great and that an 
atmospheric effect might have been partly responsible 
for the range. 

In support of Pettit's doubts, Bernheimer [15] found 
an annual trend in Pettit's data, and indicated that the 
observed variations may have been due to changes in 
atmospheric transmission, rather than to increased 
solar emission. As we shall see later, this difficulty of 
extrapolating through the earth's atmosphere is also a 
continual worry in determinations of variations in the 
solar constant. 

Visible and Infrared Radiation. The fluctuations in 
ultraviolet radiation seem to be related to hot, bright 
areas, for example, faculae and flocculi [9]. These areas, 
which can be seen visually, cover rather small portions 
of the sun. As the temperature of a body increases, the 
intensity of the emitted radiation increases at all wave 
lengths, but the wave length of maximum intensity 
shifts towards shorter wave lengths. Hence, since the 
maximumi intensity occurs at a wave length of about 
4700 A in the average solar spectrum (Fig. 1), it might 
be expected that, as the sun's temperature increases, 
the relative increase of intensity at X < 4700 A will be 
greater than in the longer wave length visible or infra- 
red regions. Such is indeed the case; the intensity of the 
radiation in the visible and infrared changes by small 
amounts in response to the dark and bright markings 
on the sun. 

Abbot [3, Vol. 6, p. 165] found that, on days with 
high solar constant, 7ox at 0.35 m increased by about 5 
per cent over its value on days with low solar constant. 
At 1.7 p., /ox decreased by about 1 per cent under the 
same circumstances. It should be noted, however, that 
solar-constant variations are not well correlated with 
sunspots [8], 

Radio Waves. As stated earlier, radio-wave emission 
from the sun (from a few centimeters to a few meters in 
wave length) indicates temperatures of 10*K; under 
disturbed conditions, radiation corresponding to lO'K 
can be observed [60, p. 328]. However, the amounts of 
these energies are very small. 

Summary. There is good evidence from radio meas- 
urements that large fluctuations in solar radiation occur 
at X < 1000 A and at X = 10 to 10' cm. The variations 
seem to appear in daily measurements and also appear 
systematically in the sunspot cycle. In the meteorologic- 
ally important spectral region of 2000-2800 A there is a 
suggestion that at least short-lived large fluctuations 
may occur (SID) [79]; chrect measurements of these 
fluctuations to determine their magnitude would be 
very desirable. At somewhat longer wave lengths, for 
example 3200 A [68], measurements indicate solar- 
controlled fluctuations, but doubts have been raised 
about the reality of their magnitude. That variations in 
the visible spectrum from parts of the sun occur can be 
seen from the bright and dark areas on the sun. How- 



ever, these areas are small and the variations in the 
visible and near-infrared radiation represent only a 
small percentage of the average radiation from the 
entire sun. 

The Solar Constant. So far we have discussed the 
relative spectral distribution of intensity in solar radia- 
tion. To describe the radiation it is also necessary to 
specify the amount of radiation on an absolute basis. 

The "solar constant" is a measure of the total amount 
of heat which reaches the outer atmosphere of the earth. 
Specifically, it is often expressed as the amount of 
energy which, in one minute, reaches a square centi- 
meter of plane surface placed perpendicular to the sun's 
rays outside our atmosphere when the earth is at its 
mean distance from the sun. 

Methods of Measurement. To clarify the following dis- 
cussion let us review the basis for the fundamental (or 
"long") method of the Smithsonian Institution for 
measuring the solar constant [3, Vol. 6, p. 30]. The 
intensity I\ of parallel monochromatic energy trans- 
mitted through the earth's cloudless atmosphere is 
given by 



or 



h = /oxe"*^"" = /ox ax", 



In 7x = In /ox + to In ax. 



(4) 



where k\ is the extinction coefficient, ax is the atmo- 
spheric transmission with the sun in the zenith, and m 
is the optical air mass or the path length of the parallel 
light through the atmosphere measured in terms of the 
zenith path as unity .^ 

Except for large zenith angles Z, the value of m is 
given by sec Z. Hence to can be readily determined; I\ 
is measured in relative units. If a\ remains constant, 
then by equation (4) a graphical plot of In I\ against 
TO will yield a straight line whose slope is In a\ and 
whose intercept for m = (outside the atmosphere) is 
In /ox; /x is measured nearly simultaneously for the 
spectral region 0.34 yu < X < 2.5 m- This is repeated for 
several values of to, so that by the graphical method 
just mentioned /ox can be evaluated at several wave 
lengths in the region. From the measurement and 
graphical extrapolation, a plot of I\ vs. X, and another 
plot of /ox vs. X can be made in relative units for the 
region 0.34 /i to 2.5 fi. We desire to find the areas 2/xAX 
and S/ox AX, respectively, under these graphs in abso- 
lute units. Therefore, by means of a pyrheliometer, a 
nonspectral measurement in absolute energy units is 
made of the total radiation /; / includes not only the 
energy which reaches the observer for X between 0.34 fi 



2. The value of m is ordinarily specified as unity for zenith 
path length at sea level. Values of m at sea level are given by 
sec Z for values of Z (sun's zenith distance) up to 70°; for larger 
Z, Bemporad's formula [56] is commonlj' used. To compute the 
air mass irip for elevated stations where the pressure is p, the 
sea-level value of m is multiplied by p/po where po is the sea- 
level pressure. When I\ is measured at one station, however, it 
is not necessary to correct tn for pressure to find /ox from 
equation (4). 



18 



RADIATION 



and 2.5 n, but also the energy for 0.29 /n < X < 0.34 /i 
and X > 2.5 /u (since energy below 0.29 m does not reach 
the ground). Hence, if to the area SIxAX under the 
spectral curve is added the energy e in the wave lengths 
which reach the ground but are not measured spectrally 
(namely 0.29 /i < X < 0.34 jit and X > 2.5 m) then the 
area under the curve, e + S/xAX, will be proportional 
to the corresponding pyrheliometric measurement I. 

The area loa under the curve of 7o\ versus X (for 
0.34 /i < X < 2.5 ix) can now be converted to energy 
units, since 



I_ 



S/xAX + t 
S/oxAX ■ 



(5) 



It remains to add to loa the energy eo for X < 0.34 n 
and X > 2.5 /i in order to obtain 7o, the solar constant. 

This "long" method implies that ox is constant dur- 
ing the period of measurements (2-3 hr), and also that 
7, the pyrheliometrically measured radiation, is known 
in absolute units (langleys per minute). In practice the 
corrections for all unmeasured spectral regions are 
applied together. 

Equation (4) requires that the atmospheric trans- 
mission ax be constant during a series of spectral meas- 
urements which are performed during a period of a few 
hours (from air mass 5.0 to 1.5). To the extent that ax 
is not constant, errors will be introduced in 7ox and 
hence in the solar constant. Partly for that reason, the 
Smithsonian Institution devised a "short" method for 
measuring the solar constant. In this method, a\ is de- 
termined by a measurement of the brightness of the sky 
in the vicinity of the sun and from an empirical rela- 
tion between the brightness and the transmission coef- 
ficient a\. 

The Numerical Value of the Solar Constant. Let us 
consider 7. The standard of pyrheliometry adopted by 
the Smithsonian Institution in 1913, when applied to 
solar-constant measurements, leads to 1.94 ly min~^ as 
the average value for 7o. This is the value most often 
used at present. The Smithsonian standard was known 
to be about 3.5 per cent higher than the Angstrom 
standard, but in 1932 and on subsequent occasions 
Abbot and Aldrich redetermined their standard and 
found that their 1913 standard was too high by 2.3 
per cent [12], thus decreasing the disagreement with the 
Angstrom scale. The new Smithsonian standard scale 
reduces the value of the average solar constant from 
1.94 to 1.90 ly min-i. 

Before accepting this new value we should examine 
the corrections applied to the solar constant for the 
unmeasured spectral radiation [3, Vol. 5, p. 103]. In 
practice a correction is made for the umneasured radia- 
tion in the interval 0.34 ;u > X > 0.27 ju, and for this 
spectral region about 3.4 per cent of the total measured 
radiation is added. Apparently no energy is added for 
radiation below 0.27 ix. A composite curve of the 55- 
km rocket measurement and Smithsonian surface meas- 
urements indicates that the region from 0.34 n to 0.27 /x 
comprises 2.9 per cent of the area between 0.34 /i and 
2.5 IX and that about 0.5 per cent of the total radiation 
is included between 0.22 ^ and 0.27 ^ [56]; hence the 



energy ordinarily added for X < 0.34 n is about right. 
We have assumed here that the 55-km rocket observa- 
tion represents 7ox for X < 0.34 ix. 

In the infrared, 2 per cent is added for radiation be- 
yond 2.5 IX during Ig determinations. For a black body 
at 6000K this should amount to about 3.1 per cent. 
Hence if the energy beyond 2.5 n is that of a black body 
at 6000K or more [5, 63], it would appear that a some- 
what greater amount than 3.1 per cent is the necessary 
correction. 

The area S7xAX is adjusted to agree with 7 by esti- 
mating the unmeasured spectral energy. In this process 
of adjustment, errors in the estimated correction are 
offset somewhat by the adjustment mechanism itself. 
This adjustment process, however, does not account for 
errors in eo in the spectral regions which cannot be ob- 
served at the ground. It is difficult therefore to say 
exactly what effect the substitution of new corrections 
would have on 7o. As a first approximation we might 
assume that the ultraviolet correction is about right 
and that the infrared correction is too low by 1 or 2 
per cent, so that the computed solar constant can tenta- 
tively be given by 1.90 < 7o < 1.94, the range making 
some allowance for the uncertainty of the corrections. 
On the basis of the Smithsonian measurements there 
does not seem to be much justification for a solar con- 
stant of more than 2.0 ly min~'.^ 

Variation of the Solar Constant. We turn now to a 
consideration of the following questions: (1) Does the 
"solar constant" vary with time? and (2) Do the 
measurements of 7o indicate the actual variation? The 
controversy regarding these questions has been raging 
for a long time, and a definite answer to the second 
question cannot yet be given. The state of the con- 
troversy is shown in a criticism by Paranjpe [67] and a 
reply by Abbot [1]; Waldmeir [77] has summarized 
some of the earlier arguments. Two main points have 
been at issue: (1) Do the measured values at two or 
more widely separated stations vary in the same way 
with time? and (2) Do the 7o measurements or the 
transmission coefficients a\ vary seasonally? If so, one 
would expect that the earth's atmosphere is introducing 
the variations and that they are not true solar changes. 

Abbot has pointed out on several occasions that the 
data from the various stations do agree for monthly 
means, but that daily values show appreciable de- 
partures. Paranjpe [67] states, however, that the data 
from the stations undergo statistical adjustment in such 
a way as to make the data between stations comparable. 
From this view, of course, interstation correspondence 
would have no significance. Abbot [1] states definitely 



3. Karandikar [50] assumed a value of more than 2.0 ly 
min~^ At the Ionospheric Physics Conference held at State 
College, Pennsylvania, in July, 1950, Dr. M. O'Day announced 
that a measurement from a rocket indicated a value of more 
than 2.0 ly min~i. This measurement has apparently not yet 
been completely checked. See Discussion of the paper "Physical 
Characteristics of the Upper Atmosphere" by T. R. Burnight 
in "Proceedings of the Conference on Ionospheric Physics 
(July 1950)." Geophys. Res. Pap. , Air Force Cambridge Research 
Laboratories, Cambridge, Mass. (1951) (in press). 



SOLAR RADIANT ENERGY 



19 



that this is not the case, but that the data are inde- 
pendent. It should be pointed out, however, that ques- 
tions regarding the accuracy of data from all solar- 
constant stations except Monteziuna have been raised 
from time to time by Abbot and his colleagues, es- 
pecially regarding the data prior to 1920 [8]. 

With regard to the seasonal variation of solar con- 
stants. Abbot has made comparisons of differences be- 
tween solar-constant measurements at Southern Hemi- 
sphere and Northern Hemisphere stations on a monthly 
basis and finds no seasonal variation in the differences. 
The season being opposite in the two hemispheres, this 
would indicate lack of seasonal variation in 7o. Although 
he foimd no twelve-month period in /o variations. 
Abbot has found fourteen other different periods in the 
solar-constant variations. Paranjpe questioned the ex- 
istence of these periods, but Sterne [73], while sup- 
porting Abbot's claim as to the statistical significance 
of some of his periods, found a strongly significant 
period of twelve months, suggesting a possible terres- 
trial effect. 

We see therefore that there has been considerable 
controversy regarding the reality of the variations 
shown by the solar-constant measurements, and nu- 
merous additional arguments, pro and con, could be 
unearthed. But the present state of affairs can be 
summed up as follows: The energy emitted by the sun 
does change from time to time. This is indicated by the 
changes which can be seen in the sun's surface and by 
the changes revealed by the ionospheric and radio 
measurements. However, the percentage change in the 
total energy output is small, amounting at most to 1 
or 2 per cent [3], and whether the solar-constant meas- 
urements as observed from the earth's surface are 
sufficiently accurate to reveal the time and/or magni- 
tude of such variations is still a debatable question. 

This controversy may be resolved in several ways. 
The surest way would be to make the measurements 
from a satellite stationed outside the earth's atmo- 
sphere. If rockets could be adequately equipped, fre- 
quent measurements from them would also be 
satisfactory. Perhaps balloons may serve for this pur- 
pose. But if these methods are economically or experi- 
mentally remote, the establishment of a few additional 
surface stations might help. In science, important 
results ordinarily are not finally accepted until they 
have been corroborated by independent observers. Here 
too, if the questions raised as to the amount and time 
variations of the solar constant are to be answered, any 
additional stations should be operated by independent 
observers, as was long ago suggested by Marvin [58]. 

However, there is a more important parameter to 
measure than the variation of Jo; that parameter is 
the earth's albedo. From the meteorological viewpoint, 
the predominant interest is not in Jo variations as such, 
but in the amount of energy absorbed by the earth and 
its atmosphere, and in the variations of this amount. 
As will be shown later, the solar energy reflected by the 
planet Earth varies so much that the energy absorbed 
may vary by ±15 per cent or more from the mean 



absorbed energy. This is to be compared with a pos- 
sible change of ±1 per cent in the solar constant. 

Extraterrestrial Solar Energy on a Horizontal Sur- 
face. Of fundamental importance for meteorology is 
the energy Q which reaches a horizontal area at the 
earth's surface. For purposes of comparison and to 
permit certain computations of Q, Milanl'covitch [61J 
computed Qe, the extraterrestrial value of Q, from the 
relation 






cos Z dt. 



(6) 



where h is the time of sunrise, h the time of sunset, Z 
the sun's zenith distance, and p the radius vector of 
the earth. If we take 7o = 1.94 ly min~\ Qb, in langleys 
per day, is given in Fig. 3. 



MAR APRIL MAY JUNE JULY AUG SEPT OCT 




JAN, FEB. MAR. APRIL MAY JUNE JULY AUG SEPT. ,OCT. NOV. DEC. 

Fig. 3. — Solar radiation on a horizontal surface outside the 
earth's atmosphere (ly daj'~'). {After List [56].) 

TERRESTRIAL EFFECTS ON SOLAR RADIATION 

Having considered the amount and the spectral in- 
tensity of extraterrestrial solar energy, we turn now to 
the effect which the earth and its atmosphere have 
upon the incident radiation. In general the atmospheric 
elements absorb and scatter part of the incident solar 
energy. 

Absorption. At the outset it should be noted that X 
< 2900 A (approx-imately) is not observed at the 
ground; nearly all energy of X < 2900 A is absorbed 
and a small part is scattered back to space by the gases 
of the atmosphere. 

The Ionosphere and Ozmiosphere. Energy of X < 
1000 A is highly absorbed by 0, Oj, or N2 [62]; such 
energy is responsible for the ionization and heating of 
the ionospheric regions. For energy in the region from 
1300 A to 3500 A, Craig [21] has made a thorough study 



20 



RADIATION 



of the available absorption-coefficient measurements 
for O2 and O3; these absorption coefficients appear 
else-svhere in this Compendium.* 

In equation (4), kx is the extinction coefficient; it 
includes the effect of both absorption and scattering. 
We can write 

(7) 



h 



a\ + Sx, 



where ax is the absorption coefficient and sx is the scat- 
tering coefficient. In places where sx is small, such as 
at high elevations in the atmosphere, the transmission 
can be written approximately 



h = /ox IO- 



CS) 



where ax is the decimal absorption coefficient, and x 
is the path length through the absorbing gas. The 
amount of absorbed energy is 

la = SC/ox - /x)AX = 2/ox(l - 10-°^")AX. (9) 

In the case of ozone, computations of la have usually 
been based on the distribution of /ox in a black body at 
6000K and give /„ ~ 0.06 h- However, as indicated 
above, /ox in the ultraviolet is considerably less than 
the value for a black body at 6000K. Therefore, h is 
correspondingly smaller. If one accepts the 55-lvm V-2 
rocket and Smithsonian spectral measurements for /ox, 
then la ~ 0.02 h [30]. Should further measurements 
verify still lower values of /ox [35, 55], /„ for ozone will 
have to be reduced even more. 

Obviously, the assumption of 6000K black-body in- 
tensities will also yield values for the absorption at 
specific altitudes in the ozonosphere which are too large. 
Thus computations such as Karandikar's yield values 
that are too high for ultraviolet absorption [50] ; Gowan 
[36] shows the effect of the lower absorption on the 
temperature of the air. 

In addition to its absorption in the ultraviolet, ozone 
absorbs small amounts of solar energy in other spectral 
regions. One of these, the Chappuis band, extends 
through the visible region from 4400 A to 7600 A and 
has a peak at 6000 A. The absorption coefficient is, 
however, so much smaller than that in the ultraviolet 
that, despite the much higher solar intensity, the total 
absorption in the Chappuis band is about 0.007/o. 
In the infrared, absorptions are centered at 4.75 /x, 
9.6 n, and 14.1 n, but /ox is so small at those wave lengths 
that almost no energy is absorbed [50]. 

Spectral Absorption by Wafer Vapor. Among the at- 
mospheric gases, water vapor absorbs the largest 
amount of solar energy, and for the most part our 
knowledge regarding these water-vapor absorptions is 
due to Fowle [26, 27]. For X > 0.9 m, energy is absorbed 
by water vapor with varying intensity in wide bands. 
Figure 4 shows the positions of these bands^ up to 
about 2.1 fi and includes two bands (B and A) for 



4. Consult "Radiative Temperature Changes in the Ozone 
Layer" by R. A. Craig, pp. 292-302. 

5. The band labelled Q reallji- includes three bands, namely, 
fi plus two small bands wi and a-i. 



oxygen absorption; Fig. 5 shows the fractional trans- 
mission of energy in the band widths indicated by 
broken arrow-headed lines at the bottom of Fig. 4. 
In addition to the bands shown in Fig. 4, several weak 
lines appear below 0.7 /x, and very strong absorption 
bands appear beyond 2 ju and particularly near 6 /i. 

WAVELENGTH (MICRONS) 



0.624 
0.686 


3- ■« 

D t 
C 


D CD < 
D 0> 

i 6 


1.302 
1.452 
1.603 
1.738 
1.870 
2.000 
2.123 


Z' 


r\l 


V \- > 


N, 


















B 




\ 


V 


















A^ 




\ 




\ 

\ 




















v 




n 


\ 




















1 






























r 




^ 

\""^ 


















1/ 






V 


A(^ 



a 0.8;i p ^ t a ' 

Fig. 4. — Location of absorption bands of oxygen (A and B) 
and of water vapor. {After Fowle [26].) 



o .90 



.80 



< .70 



=1 .60 



.50 



.40 







=.^ 












\ 


V 








^=^ 


0.8/1 


^^ 






^^ 




^^^ 








\ 




■-^ 






^^ 


^-S— 
^~?~~- 


====: 


\ 












ni 












^ 


. 


* 







2 3 4 5 6 7 8 

PREGIPITABLE WATER VAPOR, w (CM) 



Fig. 5. — Fractional transmission of solar radiation by 
water-vapor absorption bands as a function of precipitable 
water vapor. {After Fowle [26].) 



Fowle [27] measured the absorption in the regions 2-9 /i 
and some of his results are given in Table II. 

Fowle's data were measured at atmospheric pressure. 
It has long been recognized that the fractional absorp- 
tion by a water-vapor band depends on the total pres- 
sure of the air; and laboratory pressure measurements 
on two water-vapor absorption bands have recently 
been made, although the two sets of measurements 
lead to somewhat different results. Drummeter and 
Strong [24] examined the maximiun and miniraimi ab- 
sorption points in the 1.85-m band and found that ab- 
sorption at the maximum points (1.82 /i and 1.88 /i) in- 



SOLAR RADIANT ENERGY 



21 



creased linearly Avith p^'. For the minimum points 
(1.87 IX and 1.90 m) the same pressure relation existed up 
to p = 400 mm Hg; for higher pressure the absorption 
increased more slowly as p''' increased. For each of 
the entire bands at 1.35 ju and 1.85 /.i, Chapman, Howard, 
and Miller [19] find that the fractional transmission in- 
creases as a nonlinear function of (p + pwY'* where 
Pu, is the partial pressure of the water vapor. They do 
not graph their functional absorption relation explicitly 
as a function of pressure. 

Table II. Pee Cent Absorption of Radiation by Water 

Vapor 

(After Fowle [27]) 



Wave-length interval 


Precipitable water vapor 


(m) 


0.008 cm 


0.082 cm 




% 


% 


1.3 -1.75 


6.1 


18 


1.75-2.2 


13.6 


29 


2.2 -3.2 


23.6 


41 


3.2 -4.0 


21.7 


37 


4.0 -4.9 


32.5 


50 


4.9 -5.4 


18 


42 


5.4 -5.9 


47 


85 


5.9 -6.4 


64 


97 


6.4 -7.0 


68 


97 


7.0 -8.0 


25 


62 



The amount of solar energy beyond 3 m is of course 
very small, and hence the absorption of that energy 
cannot greatly affect the temperature of the atmo- 
sphere. Karandikar [50] shows the amount of absorp- 
tion in langleys per second in the various wave-length 
bands as a function of precipitable water vapor w for 
values of w from 10~* cm to 1 cm and for bands in the 
region from 0.9 /i to 8 m; he also gives the total amount 
of energy absorbed by water vapor in the stratosphere 
and shows that above 40 km the absorption is practic- 
ally zero, but that at 30 km it approaches absorption by 
ozone (especially since the ozone absorption given is 
probably too high). 

It should be pointed out that the data of Fig. 5 may 
not be used with Beer's law in the customary absorp- 
tion computations, since the bands are too wide to be 
considered as monochromatic; the empirical data of 
Fig. 5 must be utilized. However, for many purposes 
the use of Beer's law will lead to practical results [63]. 

A few transparent regions exist in the far infrared. 
The region near 10 /x is relatively transparent with re- 
gard to water-vapor absorption, and although very 
little solar energy is available in this region, it has been 
used to measure atmospheric ozone which has an ab- 
sorption band near 9.6 fx. Adel has found that the 17-24 n 
region is also relatively transparent. 

Total Water-Vapor Absorption. In order to determine 
the temperatm-e change in the atmosphere produced by 
absorption of radiation by water vapor, a summation of 
absorption over all wave lengths is required, and such 
summations have been computed by several authors. 
For example, using Fowle's absorption data, Kimball 
[52] computed the total absorption as shown in curve 
(16), Fig. 6. The curve shows the fraction of /o absorbed 



by water vapor as a function of the water vapor in the 
sun's spectral path, that is, as a function of mw. By 
using data similar to these absorptions, Tanck [74] 
computed temperature rises of about 0.1-0.7 centi- 
grade degrees per day at Hamburg depending on the 
season and the height (up to 6 km) . The order of magni- 
tude of the absorptions given by Tanck's equation 
agrees with airplane measurements [29]. 

Clouds. Thanlis to Fowle and to some recent studies 
[19, 24], the status of water-vapor absorption is fairly 
well known; however, the absorption of solar energy by 
clouds is comparatively unknown. A few theoretical 
estimates have been published [45], but very few meas- 
urements have been made. 

One method of measuring the amount of energy ab- 
sorbed is to measure simultaneously, with pyrheliom- 
eters, the energy leaving and entering the cloud layer 
both at its upper and lower surfaces; the difference be- 
tween the energy which enters the cloud and that 
which leaves it is the amount absorbed. Neiburger [66], 
using one blimp on which to mount two pyrheliometers, 
one facing upward and the other downward, made 
many Vertical traverses through stratus clouds. When 
the blimp was below the clouds, he estimated the up- 
ward- and downward-flowing radiation at the top of 
the cloud. Because he lacked a second blimp, simul- 
taneous measurements could not be made both below 
and above the cloud, and since the albedos of clouds 
vary appreciably over short distances and times, errors 
may have been introduced because of the lack of simul- 
taneity. At any rate, Neiburger's measurements, which 
were probably the first absorption measurements made, 
indicate that in the mean about 5 to 9 per cent of the 
incident radiation is absorbed in stratus clouds, and 
that there may be large variations from the mean. 

To measure the absorption in other types of clouds, 
especially over extensive cloud decks, the United States 
Weather Bureau, through the cooperation of the Air 
Force and the Office of Naval Research, has made 
measurements using B-29 airplanes as platforms for 
the two pyrheliometers. On a few occasions two air- 
planes, each equipped with two pyrheliometers, have 
been flown, one vertically above the other, with the 
cloud deck between them. When only one airplane was 
available, the plane, carrying two pyrheliometers, was 
flown above the cloud deck and above a pyrheliometer 
which was located on the ground. In the absence of 
ground snow cover, a good estimate can be made of the 
albedo of the ground; or if the ceiling is not too low, 
the albedo of the ground can be measured by flying the 
airplane below the clouds. Preliminary results from 
these measurements indicate that the absorption by 
these deep widespread systems averages about 20 per 
cent of the solar radiation incident on the cloud. ^ These 
measurements are still few in niunber and should be 
verified by additional determinations. 



6. Reported bj' T. H. MacDonald at the January 1950 meet- 
ing of the American Meteorological Society in St. Louis, 
Missouri. 



22 



RADIATION 



This amount of absorption is much higher than the 
maximum of 6 per cent which Hewson's theoretical 
computations indicate [45]. If it is assumed that the 
measurements are correct, the discrepancy can be at- 
tributed to several factors. Clouds are complex aniso- 
tropic physical entities, and the theory must make 
numerous assumptions to handle even isotropic clouds 
of liquid water drops. In particular, the theory does not 
include absorption by water vapor in clouds. A cloud 
whose liquid-water content is 0.5 g m~' could easily 
contain 5 g m~^ of water vapor, and 10 g m~^ or more 
are quite possible. Hence with the radiation undergoing 
numerous reflections by the liquid water drops, the 
path length of a ray through the water vapor could 
easily be 10 to 20 times that of its path through liquid 
water. Furthermore, the fractional absorption of water 
vapor is by no means negligible by comparison with 
that of liquid water [6]. The absorption by the water 
vapor might therefore be comparable with that by 
liquid drops. Such an effect would bring computations 
such as Hewson's more in line with the measurements. 

Another factor is absorption by the ice and snow par- 
ticles which exist in cirrus and altostratus clouds. The 
mechanism of such absorption is unlcnown and has not 
been included in theoretical discussions. In view of these 
and other theoretical complexities, measurements for 
many types of clouds are required to establish firmly 
the magnitude of absorption by clouds. Apparently, 
relatively diffuse thick clouds (such as altostratus) will 
reflect a smaller amount of energy than less diffuse 
thick clouds, such as stratus or stratocumulus clouds 
of the same or even smaller vertical thickness [18, 32]. 
Mecke [59] has pointed out that, for infinitely thick 
clouds, high reflection will be associated with low ab- 
sorption and vice versa. These ideas are in qualitative 
agreement wiih the relatively low absorption in thick 
stratus with its high albedo [66] and with the relatively 
high absorption in thick altostratus of extensive cloud 
systems with its low albedo. 

The Earth's Surface. The energy which reaches the 
surface of the earth is either absorbed or reflected. The 
albedo of the earth's surface will be discussed later; it 
is the order of magnitude of the absorbed energy which 
should be emphasized here. In middle latitudes, at 
least, during cloudless conditions about 80 per cent of 
the energy Qe incident in a day at the outer atmosphere 
reaches the ground. Except for snow-covered areas, an 
albedo of 10 per cent may be assumed for purposes of 
rough evaluation. Hence under these conditions, about 
72 per cent of Qe is absorbed by the earth's surface. 
This is very much larger than the absorption of 2 per 
cent by ozone, or of about 8 per cent by water vapor, 
or even of the 20 (?) per cent by extensive cloud sys- 
tems. Of course, in overcast areas, the energy which is 
absorbed by the ground is smaller than 70 per cent and 
may be equal to or less than the energy absorbed in the 
cloud. But with average cloudiness, the ground ab- 
sorption approaches about 50 per cent of the extra- 
terrestrial radiation. 

Therefore, although absorption by ozone may cause 
large temperature changes at 40 km because of the low 



atmospheric density at that height, by far the largest 
amount of energy which potentially becomes available 
for atmospheric processes is absorbed by the earth's 
surface itself. 

Miscellaneous Absorptions. Several gases absorb 
minor amounts of solar energy. Oxygen, in addition to 
the important absorptions in the ionosphere and ozono- 
sphere, has some minor absorptions in the near infrared 
(Fig. 4). Nitrogen compounds and CO2 absorb small 
amounts. Carbon dioxide is, of course, of great im- 
portance in long-wave terrestrial radiation, but plays a 
minor role in solar radiation absorption [50]. The pres- 
ence of methane has recently been announced by several 
authors [54]. Its role in the heat balance of the atmo- 
sphere has not yet been considered. 

Scattering. In the absence of clouds, energy is de- 
pleted from the direct solar beam through absorption 
and scattering by air molecules, water vapor, and dust. 
Where absorption is negligibly small the scattering coef- 
ficient may be expressed as 



Sx = Sa\ + Swh + Sd\, 



(10) 



where Sa\, s„x, and Sd\ are the scattering coefficients of 
pure dry air, water vapor, and dust, respectively. 

Spectral Molecular Scattering. When the isotropic par- 
ticles which cause scattering of energy are very small 
by comparison with the wave length of the light (< 
0.1 X), the theory developed by Rayleigh [34] shows that 
the scattering coefficient depends on X~* or, if the mass 
of air in the vertical at sea level is taken as unity, 



SaX = 



327r'(nx - 1?H\- 



3Na 



(11) 



where n\ is the index of refraction of air for light of 
wave length X, A''^ is the number of molecules per cubic 
centimeter of air, and H is the height of the homogen- 
eous atmosphere. 

If scattering by air molecules alone is considered, the 
monochromatic energy which reaches sea level as the 
original parallel beam is given by 



h = /ox exp(-s„x sec Z). 



(12) 



Values of sa and of the transmission a^x = /x//ox for 
the Rayleigh scattering law are given by List [56]. 
For air molecules which are not spherical it might be 
necessary to multiply those values of Sa\ by 1.04 [76]. 

Total Molecular Scattering. We are often interested 
not in the spectral transmissions but in the total trans- 
mission I/Io. If equation (12) is integrated, we see that 



I/h = (I//0) f h 
Jo 



dk 



(l/7o) / /ox exp( — Saxm) rfX. 
Ja 



(13) 



The data for /ox are available from Smithsonian Insti- 
tution measurements (Fig. 1), and several authors have 
computed ///o from equation (13). Figure 6 shows such 
a computation by Kimball [52]. Curve (1), for iw = 0, 



SOLAR RADIANT ENERGY 



23 



is in excellent agreement with Linlce's results [55, p. 
248]. 

Spectral Scattering by Water Vapor. The atmosphere 
is, however, never pure nor dry; both dust and water 
vapor are ever present in varying degree. Fowle [28] 
examined the transmission of the atmosphere at wave 
lengths where water vapor does not absorb. At those 
wave lengths, if dust is neglected, 



h = /ox exp(— Saxm) exp( — s„xwm) 



= /ox (a„xfCx)'" = /oxax. 



(14) 



Here the transmission coefficient through one dry at- 
mosphere at vertical incidence is given by aa\ = 
exp( — Sax) and thi'ough one centimeter of precipitable 
water vapor by a-„.,x = exp( — s„x). From equation (14) 



or 



a\ = aaxflffiX, 



In a\ = In a^x -f- w In a„x. 



(15) 



(16) 



A plot of In a\ against w should yield a straight line 
whose slope is In a„\ and whose intercept at t« = is 
In aa\. Hence, a„x and aa\ can be determined. 

As might be expected, for a given X the observed cor- 
responding values of In a\ and w do not fall exactly on 
a straight line. In order to remove random fluctuations 
Fowle compiled average values, but it is not clear 
whether he averaged values of a\ or of In a\. At any 
rate, Fowle plotted his average In a\ against w. The 
points still scatter quite a bit, but the "best" straight 
line was drawn through the data, and the correspond- 
ing flax and a„x were determined. His values of a„x are 
given by List [56]. 

Fowle [28] assumed that the X~^ law (equation (11)) 
applied also for scattering by water vapor and found 
that his transmission coefficients a^,\ were such that 
the scattering is greater than might be expected from 
the number of water-vapor molecules. He concluded 
from this that the water vapor existed as aggregates of 
water-vapor molecules (see also [76]). Moon, however, 
using Fowle's data, plotted the logarithm of the average 
a„\ against In X, and found that 



flwX 



x-2. 



(17) 



Any relation between a,„x and X (such as equation 
(17)) should apply for a single set of measurements of 
ttyix . It seems necessary therefore to plot In X against 
In a„x and not against In a^x- Differences in their pro- 
cedure perhaps account for the difference in the wave- 
length laws obtained by Moon and by Fowle. 

It should be pointed out that Angstrom [11] ques- 
tioned the validity of assuming that the water vapor 
was the actual scattering agent. If dust and water- 
vapor advection usually occur together so that an in- 
crease in one accompanies an increase in the other, it 
may be the dust which is actually perfoi-ming the scat- 
tering. However, Fowle evaluated the effect of dust in 
his data, and found it to be only about one-half of 1 per 
cent for ax and 2 per cent for aa\ [28]. As these con- 



flicting views indicate, the wave-length dependency of 
water- vapor scattering is not very well known. 

Total Water-Vapor Scattering. Here again the total 
transmission is often desired in lieu of the spectral 
transmission. With the aid of Fowle's data for a^x and 
Qwx, Kimball [52] computed the fractional transmission 
of solar energy at normal incidence through a dustless 
atmosphere for various values of w. The computations, 
which include scattering but exclude absorption, are 
shown in Fig. 6 by the dashed curves (1) through (8) 
for values of w up to 6.0 cm. By adding the depletion 
due to water-vapor absorption, Kimball computed the 
transmissions shown in curves (9) through (15); the 
latter curves include the effect of both scattering and 
absorption. 



AIR MASS, m ( PRESSURE-76.0 cm.) 
1.0 2.0 '3.0 




Fig. 6. — Fractional transmission of solar energy through 
the earth's atmosphere. Curves (l)-(S), scattering only; 
curves (9)-(15), scattering plus absorption by precipitable 
water vapor (w) amounts shown on curves; curve (16), frac- 
tional absorption by water vapor as a function of wm. {After 
Kimball [52].) 

Dust. There remains the scattering from the direct 
solar beam by dust. Angstrom [11] has derived a law 
for dust extinction,' 



Sd\ = |8X 



(18) 



where |S is a constant representing the number of scat- 
tering particles, and y another constant representing 
the size of the scattering particles. Angstrom describes 
graphical methods for obtaining /3 either from a total 
radiation measurement or by filter measurement. By 
analyzing the spectral measurements of the Smith- 
sonian Institution, he found y = 1.3 on the average. 
From laboratory measurements of the relation between 
7 and the size of scattering particles, he showed that 
the average size of the scattering particles was 1 /i. Ives 
and his co-workers [48], however, have found from ac- 
tual particle measurements near the ground in cities 
that the most frequent diameter size is near 0.5 /x. Their 



7. Angstrom's extinction coefficient, here designated by Sd\, 
includes scattering by water vapor, but not absorption. 



24 



RADIATION 



findings are valid only for particles larger than 0.2 ^ in 
diameter because their microscope could not detect 
smaller particles. Recently Crozier and Seely [22], mak- 
ing measurements from airplanes, found the greatest 
frequency of particle diameter in the free air to be 3-6 ii ; 
their instruments could not catch the smaller particles 
efficiently. Linke and von dem Borne [55] showed that 
7 varied A\'ith the altitude of the observing station and 
from place to place. In general, for higher altitude and 
less smoky areas, y was larger than elsewhere, and 
hence the average particle size was smaller. 

All these are average values, and both (3 and 7 vary 
with time even at one observing station, for the num- 
ber, size, and shape of the scattering particles vary con- 
tinually. Also, at any time the whole spectrum of par- 
ticle sizes ranging from below 0.2 ^ to 1 /j and larger are 
to be expected. 

This complex scattering by particles which are larger 
than molecules is a serious problem in spectral measure- 
ments. In particular, dust is troublesome in ozone 
measurements which ordinarily utilize light at 3000- 
4000 A where differential spectral scattering usually be- 
comes an important problem. Ramanathan and Kar- 
andikar [70] found that peculiar ozone effects can easily 
be produced by improper assumptions regarding dust. 
They also found, as might be expected, that 7 is not 
really constant and that in India it lies on the average 
between and 1.3 in the region 3000-4450 A. 

Another measure of the dust parameter, the "tur- 
bidity factor," was designed by Linke. He defines the 
turbidity factor r from 



where 



h = /ox exp( — fcoXTxm), 



A'axrx = ka\ + kw\iv + kd\d, 



(19) 



ka\, A',„x, and kd\ are the extinction coefficients of air, 
water vapor, and dust, respectively, and d represents 
the "quantity" of dust [55, p. 266]. He uses an "appro- 
priate" average value and integrates equation (19), so 
that 



/ = /o exp{ — kaTm), 



(20) 



where /.■„ and t now represent mean values over wave 
length. Such averages cannot really be obtained, so 
that the discussion which follows represents an ap- 
proximation. 

Let /„, designate the intensity of light transmitted 
through a pure dry atmosphere; then e"*"""' = I'm/Io- 
Equation (20) can now be written 



In /o - In 7 



ln7„ 



In I„ 



(21) 



By means of equation (21), r can readily be computed 
from a single measurement of /, for Jo is a constant 
(generally taken as 1.94) and iL can be obtained from 
graphs such as Fig. 6. 

In equation (20), t can be interpreted as the niunber 
of pure, dry air masses which would produce the ex- 
tinction observed in the moist, dusty atmosphere. It 
was found, however, [42, 55] that t was a function of m 



and thus was not a reliable measure of turbidity. To 
overcome this defect, Linke [55] decided to relate t, not 
to a dry air mass, but to a dustless air mass containing 
1 cm of precipitable water vapor. Instead of I'm. in 
equation (21), we therefore introduce lL.w=i- The 
new turbidity factor becomes 



e = $„ In (lo/I) 



(22) 



where 



$m = 



In 7o — In /,„ 



Linke's values of $„ are given in Table III. 

Table III. Values of *„ in Equation (22) 
(After Linke [55]) 



0.5 



23.35 13.57 9.607.97 



1.5 



6.04 5.02 



3.80 



3.10 



10 



2.63 



With the aid of a single pyrheliometric measurement, 
can be computed. According to Linke, it will vary 
relatively little with air mass; any observed diurnal 
variation of G will be a real variation in turbidity. 
Turbidity factors for portions of the spectrxmi have also 
been designed and can be measured with filters [55]. 

Neither Angstrom nor Linke attempted to separate 
scattering by water vapor from scattering by dust, and 
indeed, as Angstr5m pointed out, it may not be valid 
to do so. However, Kimball [52] assumed that scatter- 
ing by dust could be separated. He estimated w from 
either surface vapor pressure or radiosonde data. He 
measured I and computed the transmission a = I/Io. 
From Fig. 6, he found a^.w, the transmission through 
a dustless atmosphere containing w cm of precipitable 
water vapor. Then a^.w — a = dd, the fraction of 7o 
which is depleted by the dust. The value of dd, of course, 
varies with m. Klein [53] gives some values of dd which 
vary from to 0.09 for m = 1, and from to 0.13 for 
m = 2. 

Wexler [78] and Haurwitz [42] have discussed the 
turbidity factors of Angstrom and Linlve and conclude 
that neither is wholly satisfactory. These factors are, 
however, among the best simple methods available at 
present for determining the atmospheric turbidity quan- 
titatively. Although expressions of the total turbidity 
such as may have some specialized uses, for spectral 
measurements such as those involved in ozone and solar- 
constant measurements we shall have to know more 
about the way dust affects light of various wave lengths. 
This will probably involve determination of the size 
and number of dust particles above an observer, which 
in turn may be helpful in studies of condensation nuclei. 

Scattering by Liquid Water Droplets. Scattering of 
light by sphea-ical particles which are not very small in 
comparison with the wave length is given by the well- 
known Stratton-Houghton curve. Recently Houghton 
and Chalker [46] have extended the earlier computa- 
tion; their results appear in Fig. 7. The extinction by 
spherical water particles (refractive index 1.33) is re- 



SOLAR RADIANT ENERGY 



25 



lated to wf-NKs, or A's times their geometrical cross 
section, so that 



h = Io\exp{-2Trr'NK,), 



(23) 



where r is the radius of the drops and A'' is their number. 
Figure 7 shows K^ as a function of the parameter X 
= 2Trr/X. Equation (23) holds for nonabsorbing par- 
ticles and is valid at wave lengths where water ab- 
sorption is negligibly small; the summation is required 
over drop radii when the drop sizes are not uniform. 
For particles where /ix ^ 1.33, /v's will differ from the 
values of Fig. 7; van de Hulst [7G] shows some varia- 
tions. From Fig. 7 it is important to note that for some 
ratios of particle size to wave length the scattering does 
not always increase with decreasing wave length. 



4.0 



3.0 



2.0 




Fig. 7. — Scattering-area coefficient Ks for liquid-water 
drops in nonabsorbed spectral regions as a function of X and 
of drop radius r. {After Houghton and Chalker [46].) 



Multiple Scattering. In the case of pure Rayleigh scat- 
tering (if it ever can be said to exist in the atmosphere) 
the scattering is symmetrical about the particle so that, 
for example, the forward- and backward-scattered 
energy are equal. But as the particles become larger the 
scattering increases in the forward direction [34; 55, p. 
161]. Calculations of the effect of such particles, es- 
pecially for multiple scattering, become rather complex ; 
however they have been undertaken by several authors 
[76]. 

The energy which is scattered from the original solar 
beam will in general be scattered more than once on its 
way down to the earth's surface or else out to space. 
From an empirical viewpoint, regarding the contribu- 
tion of the cloudless sky radiation to the total radiation 
on a horizontal surface, Kimball [52] states that of the 
radiation scattered from the direct solar beam, half 
will be scattered down and half up. In a pure Rayleigh 
atmosphere this would be the case. But for the actual 
conditions of the atmosphere, it serves only as a useful 
approximation for average daily values of cloudless- 
sky radiation after the total scattering from the direct 
beam has been evaluated. 



For instantaneous values, Kimball found the ratio of 
the direct sunlight component on a horizontal surface 
/;, to the total solar and sky radiation on a horizontal 
surface Q to be a function of the zenith distance of the 
sun (Table IV). 

Table IV. Values ofIk/Q as a Function of Sun's Zenith 

IDlSTANCB Z 









(After 


Kimball [51]) 








z 

(deg) 


30.0 


48.3 


60.0 


66.5 


70.7 


73.6 


75.7 


77.4 


78.7 


79.8 


h/Q 


0.84 


0.84 


0.80 


0.78 


0.76 


0.72 


0.69 


0.67 


0.65 


0.63 



Similar values have also been found by other observ- 
ers [55, p. 356]. If we designate the diffuse sky radiation 
by D, then D = Q — /;,. As might be expected, the 
ratio D/Q increases where the atmospheric turbidity is 
high [55]. Measurements illustrating this point {e.g. 
illumination measurements) have often been made with 
instruments for relatively narrow spectral bands. It 
would be desirable to measure the ratio for nonspectral 
radiation with varying atmospheric transmissions or 
turbidity factors. 

Albedo. By the albedo of a body we mean the fraction 
of the incident energy which is reflected by the body. 
Thus the albedo A of the planet Earth is the fraction of 
the energy incident at the "outer limits" of the at- 
mosphere which is returned to space; the albedo of a 
cloud "surface" is the fraction of the energy incident 
upon the cloud which is reflected by the cloud. 

The terrestrial entities which reflect solar energy are 
(1) the cloudless atmosphere, (2) clouds, and (3) the 
earth's surface. The sum of these three reflections is the 
total energy reflected by the Earth. Expressed as a 
fraction of the extraterrestrial solar energy intercepted 
by the Earth, this sum determines A. 

The Albedo of the Cloudless Atmosphere. 1. Pure Dry 
Air. We have seen that within a few per cent the frac- 
tional spectral depletion of solar energy by molecular 
scattering is represented by the Rayleigh scattering 
law, and the summation o\'er wave length is readily 
given as a function of air mass from curve (1) of Fig. 6. 
The earth as seen from the sun can be considered as 
made up of narrow concentric circular rings centered 
about the subsolar point. To an observer in a particular 
ring the sun is at a specified zenith distance, and hence 
in each ring the optical air mass m is known. From m 
and the area of the rings, together with the above- 
mentioned relation between scattering and air mass, 
the amount of energy scattered by the entire atmo- 
sphere can readily be calculated and found to be about 
15 per cent of the incident energy [30]. This was calcu- 
lated using Fowle's data; Fig. 6 gives a slightly smaller 
value. However, this energy is scattered in all direc- 
tions. To determine the fraction scattered upward 
(away from the earth's surface) it is necessary to assume 
something about the angular scattering by each par- 
ticle. Scattering by small particles, such as molecules, 
is symmetrical about the particle [34]. Hence as much 
energy is scattered up as is scattered down. Even for 



26 



RADIATION 



multiple scattering this rule is closely obeyed. Conse- 
quently from 7 to 8 per cent of the incident solar energy 
would be scattered back by the pure, dry, cloudless 
atmosphere. 

2. Water Vapor. The scattering by water vapor and 
questions concerning it were discussed earlier. If one 
accepts 1 — a^ as the depletion by water vapor due to 
scattering, then scattering for the total spectrum can 
be computed as a function of air mass, as was done by 
Fowle, and also by Kimball (Fig. 6). From this func- 
tional relation, the scattering by water vapor over the 
whole earth can be computed. But for this, of course, 
data on the distribution of water vapor with latitude 
are necessary. From a rough estimate of w, obtained 
from the distribution of surface vapor pressure, and 
after weighting the areas of the earth involved, it is 
found that 10 per cent of the incoming solar energy is 
reflected by water vapor [30]. 

This, again, represents the energy scattered in all 
directions, but the portion which is scattered back to 
space is not so readily ascertained as it is for air mole- 
cules. Fowle believed that the scattering^particles were 
aggregates of water-vapor molecules; Angstrom sug- 
gested that dust might be the scattering agent. In either 
case, it is recognized that if the size of the particles 
approaches the wave length, the forward scattering 
exceeds the backward scattering. At any rate, two ex- 
tremes can be postulated: (1) Either half the scat- 
tered energy (5 per cent) is directed upward; or (2) 
none of the scattered energy is directed upward. 

3. Dust. Concerning dust our knowledge is most 
meagre. Not only is the transmission coefficient for 
dust in doubt, but the distribution of dust over the 
world is inadequately known. Klein [53] gives a com- 
pilation of some values which serve as a guide, but even 
these "measured" values may be inaccurate in view of 
the inadequate understanding of dust depletion. From 
Klein's data one may estimate a depletion of about 5 
per cent of the initial radiation on a world-wide basis. 
In view of the probable greater forward scattering and 
some absorption, less than 2.5 per cent is scattered 
back. An estimate of 1 per cent might be about right. 

4. Total Atmospheric Reflection. A summation of the 
reflection by atmospheric elements gives a reflection 
lying between 8 and 13 per cent, depending on how 
much is allowed for upward scattering by water vapor 
and dust. There are not very many direct measure- 
ments which yield the reflection by the atmosphere. 
In the lower layers of the atmosphere, some airplane 
measurements [29] indicate that about 5 per cent of 
the energy incident at 10,000 ft is scattered upward by 
the air below 10,000 ft. These measurements were made 
with a solar zenith distance Z of 53° on a rather smoky 
day. At greater heights and zenith distances greater 
reflection presumably would have been measured. Teele 
[75] measured the visible energy scattered back at 
72,000 ft. He interpreted his measurements as indi- 
cating that 6 per cent of the incident energy is reflected 
by the air when Z is 60°. 

These measurements and calculations are valid for 
the cloudless atmosphere only. For the average con- 



dition of 0.54 cloudiness, calculation indicates that the 
cloudless portions of the atmosphere reflect about 6 or 
9 per cent of the incident solar energy, depending on the 
assmnptions made, when about 2.7 per cent is included 
for the reflection by the air above the clouds. 

Clouds. Most of the solar energy reflected to space is 
reflected by clouds. However, the albedo of clouds is so 

Table V. Albedo of Various Cloud Types 







Albedo 


Source 


Cloud type 


(per 
cent) 


Luckiesh [57] (vis- 


Very dense clouds of extensive 


78 


ible light) 


area and great depth 






Dense clouds, quite opaque 


55-62 




Dense clouds, nearlj' opaque 


44 




Thin clouds 


36-40 


Fritz [32] (total ra - 


Stratocumulus, overcast 


56-81 


diation, exten- 


Altostratus, occasional breaks 


17-36 


sive S3'stems; 


Altostratus, overcast 


39-59 


cloud t3'pes be- 


Cirrostratus and altostratus 


49-64 


low measured 


Cirrostratus, overcast 


44-50 


clouds not speci- 






fied) 






Aldrich [7] 


Stratus, 600-1000 ft thick 


78 



variable, even for one type of cloud, and our informa- 
tion about the spatial distribution of cloud types is so 
poor that it is impossible, from individual cloud-albedo 
measurements, to specify an average value over time 
and space for the total reflection by clouds. Hence, in 
order to estimate the average albedo of clouds, it is 



yo 


1 


1 ■ 


1 ■ ■ 


1 


I 




- 








- 


H 


- 






7 V7 V 


- 


liJ 








V ' 




u 












u. 


. 








_ 


U- 

o 15 




















c/> 


V OVERCAST 


? w 


_ 


a 


D BROKEN CLOUDS 






cr 








w 




Q 


- 






VVV V 


V 


2 








V?'% V 




3 


- 








~ 


5,0 

in 


















^ V 




tn 








L ^ 




UI 


_ 








1 


2 
^ 






, , V ™, ' ->' ' 




P 


OD 


V 


w ' "' 4 " 




I 




" 




B ' 




^ 5 




' 




□ D 














Q 


ana 




9# w 


'^ 


~ 


O 


UV V □ 


V V 






D 


vo a V 


m a asav a 




~ 


<J 


' ^ffS 


a d' c?" 


|7V 




- 





1 


1 


1 


f 


1 



20 40 60 

ALBEDO OF CLOUD (%) 



80 



100 



Fig. 8. — Observed albedo of stratus clouds. {After Nei- 
burger [66].) 

necessary to measure the albedo of the whole earth 
first and then to subtract the contributions by the 
atmosphere and by the ground. The remainder is the 
albedo of clouds. 



SOLAR RADIANT ENERGY 



27 



Such a computation [30], based on lunar measure- 
ments (to be described later), indicates that the average 
albedo of clouds is about 50-55 per cent of the energy 
incident on the clouds. This value may be compared 
with several series of measurements given in Table V 
and in Fig. 8. 

It will be noted that 80 per cent seems to be a very 
high value, and that the 78 per cent which Aldrich [7] 
measured over a single stratus cloud is not a suitable 
average. According to BuUrich [18], for average clouds 
of infinite thickness the albedos by cloud types will be 
as follows: stratocumulus, 0.78; stratus, 0.74; and alto- 
stratus, 0.46. A low albedo (39 to 59 per cent) for the 
altostratus type of cloud can be seen in the measure- 
ments in Table V. 

Albedo of the Earth's Surface. The albedo of the 
ground has a very wide range of values also. In general, 
the lowest albedos occur over water. Forests or other 
configurations which can trap solar energy act nearly 
as black bodies and therefore likewise have low albedos. 
On the other hand, snow-covered terrain has a verj^ 
high albedo; values up to 90 per cent have been meas- 
ured over fresh snow. As the snow becomes older or 
turns to ice, its albedo decreases markedly, and it 
absorbs more energy. Data for several types of terrain 
are given in Table VI. It will be noted that general 
terms such as "grass" give only an approximate esti- 
mate of the albedo, so that for investigation of such 
quantities as local turbulence near the ground, the 
albedo at the time and near the place in question will 
have to be measured. 

Table VI. Albedo op Various Surfaces 
{After List [56]) 



Surface 


Albedo (per cent) 


Desert 


24-28 


Fields, various types 


3-25 
3-10 


Grass, various conditions 

Ground, bare 

Mold, black 


14-37 

7-20 

8-14 

18 


Sand, wet 


9 


Snow or ice 


46-86 


Water (direct sun* only) Z (degrees) 




2.0 


20 


2.1 


40 


2.5 


50 


3.4 


60 ... 


6.0 


70 


13.4 


80.. 


34.8 


85 


58.4 


90 


100.0 



* For reflection of sun plus sky radiation Angstrom [10] 
gives : 

Z (deg) 43.0 46.9 70.5 77.9 84.5 

A (per cent) 3.9 5.7 13.8 30.0 46.5 

The albedo of large water surfaces depends very 
largely on the angle of incidence of the light, or the 
sun's zenith distance Z. Under cloudless conditions, the 
direct solar radiation follows Fresnel's law of reflection 
very closely even when the Avind is 10 mph [10]. For 
small values of Z (sun overhead) the reflectivity is very 
low, and it is not until the angle reaches about 65° 



that the albedo for solar and sky radiation becomes as 
much as 10 per cent. Under overcast skies the albedo 
of the sea surface is about 10 per cent, but changes a 
little even then with solar altitude and cloud thickness 
[65]. When the wind velocity is large enough to cause 
whitecaps, the albedo of the water increases, and Brooks 
[17, p. 460] gives 31 per cent as the albedo when the 
water surface is rough. Angstrom states, however, that 
in ordinary geophysical problems the data of Table 
VI are applicable. 

The low albedo of water and, in general, of land 
means that the contributions of the earth's surface to 
the total albedo of the planet Earth must be small. 
As a rule, areas which are snow-covered receive little 
sunlight; the same may be said for water areas which 
have a high albedo (low solar altitudes). The net result 
is that, when the average cloudiness is considered, the 
earth's surface contributes less than 4 per cent of the 
incident energy to the total albedo of the earth; this 
contribution is probably between 2 and 3 per cent [30]. 

The Albedo of the Planet Earth. The sum of the al- 
bedos of the various entities is the albedo A of the 
planet Earth. As stated earlier, since there is a vari- 
ability of the albedo of clouds, and since clouds con- 
tribute most to the albedo of the planet Earth, A can 
be found only by measurements from or on bodies out- 
side the earth. 

Danjon [23] has made such measurements by viewing 
the moon with a suitable photometer. The moon is 
illuminated by two sources of light. The light side of 
the moon is illuminated directly by the sun; the dark 
side, by the eai'th. The light from the earth is sunlight 
which has been reflected by the earth to the dark side 
of the moon. Consequently, the brightness on the dark 
side of the moon, as compared with the brightness on 
the light side, is a measure of the sunlight reflected by 
the earth, that is, it is a measure of A. Of course, such 
measurements involve many difficulties, in addition to 
observational ones. For example, the spectral distribu- 
tion of the earth's light is different from that of sun- 
light and doubtless changes with the albedo itself. 
Hence, any selective reflectivity by the moon would 
introduce errors. Another problem is the stellar magni- 
tude of the moon. When his paper was already in press, 
Danjon learned of a new value of the moon's brightness 
which would somewhat alter his calculations. However, 
the value which Danjon originally used for the moon's 
brightness is still quoted in some astronomy textbooks, 
so his calculations may be correct. Danjon's average 
value of the earth's albedo for visible light (about 0.4 /i 
to 0.74 m) is 39 percent. But visible light comprises only 
about half, or even a little less, of the total extrater- 
restrial solar energy. Hence, to determine the total 
albedo, adjustments to his measured values must be 
made for the ultraviolet and infrared portions of the 
solar energy. Calculation of the corrections gives an 
albedo of about 28 per cent for the infrared, about 50 
per cent for the ultraviolet, and 35 percent for the total 
sunlight. The reflection in some portions of the ultra- 
violet where ozone does not absorb energy, as at 0.36 /j, 
for example, may be considerably higher than 50 per 



28 



RADIATION 



cent, which is the calculated reflection for the whole 
ultraviolet radiation (X < 0.4 fi). 

Several other estimates of A have been computed by 
assuming some value for the average reflection by 
clouds and/or by studying the average transmission to 
the earth's surface and estimating the amount of energy 
absorbed by the atmosphere and clouds. Notable among 
these calculations of A are the 43 per cent of Aldrich [7] 
and the 41.5 per cent of Baur and Philipps [14]. 

In addition to the average value of the earth's albedo, 
Danjon found large fluctuations of the albedo from 
season to season and among his individual measure- 
ments. Some average values of the visual albedo varied 
from 30 per cent in August to 50 per cent in October. 
This large variation is not too surprising. Nor does 
absence of a relation either to snow cover or cloud 
amount cast serious doubt on this albedo variability. 
The amount of solar energy incident on the snow- 
covered areas is small so that they contribute little to 
the total albedo. As for cloud amount, even if this latter 
quantity were known on a world-wide basis, it would 
not imiquely determine the contribution of clouds to 
the earth's albedo because the albedos of individual 
cloud types themselves are extremely A'ariable. 

The meteorological significance of this large albedo 
variation is obvious. If there is any possibility, as 
several authors believe, that variations in the solar 
constant of about 1-2 per cent could influence the state 
of the weather, then the much larger changes in the 
reflected energy and hence in the absorbed energy must 
be significant indeed. Only the absorbed energy can 
affect the atmosphere. Perhaps short-period changes in 
the solar constant cause changes in the earth's albedo, 
but such a causal relationship is not obvious a priori 
and would have to be established before it could be ac- 
cepted. At any rate, whatever the cause of its change, 
measurements of the earth's albedo would indicate the 
large changes in the solar energy which is absorbed and 
potentially becomes available for meteorological proc- 
esses. 

The best way to measure the albedo, as with other 
solar-variation effects, is to mount instruments on a 
satellite stationed outside the earth. In the absence of 
such a satellite, techniques similar to Danjon's must 
suffice and his results will have to be verified. Danjon's 
technique would require a little elaboration. For ex- 
ample, from measurements in France, reflections from 
the Pacific Ocean area would not influence the moon's 
dark-side illumination. Hence, measurements from 
widely separated regions would be needed to determine 
the albedo of the whole earth. Also, as stated pre- 
viously, an estimate of the ultraviolet and infrared 
albedo would also be required. However, the main 
changes in albedo from day to day would be given by 
visual albedos alone if the corrections should prove 
difficult to obtain. 

Solar Energy at the Earth's Surface. We have con- 
sidered the depletion of solar energy through scattering 
and absorption by the various constituents of the at- 
mosphere. The remainder of the direct radiation reaches 
the ground, and of course, a considerable portion of the 



scattered radiation also arrives at the ground as radia- 
tion from either clear or cloudy skies. 

Cloudless Sky. Figure 6 shows the fractional trans- 
mission at normal incidence to the sun as a function of 
air mass and of water-vapor content for a moist, dust- 
less atmosphere. Multiplication by the solar constant 
will give the transmission in absolute units. For many 
purposes it will be of greater interest to determine the 
cloudless-sky energy Qo which reaches the horizontal 



b.O 

4,5 

4.o' 

3.5 

3.0 

2.5 

2.0 

1.5 

1.0 

0.5 









,.5 


l'3 


^2 


uT 


ff\ 




p 




Im 


T] 


06 




0.3 












1 










|_ 






















1 


1 










1 








1 












\\ 


1 


1 










1 








1 


i 


\ 




ii 






1 \ 


1 










t 








1 


\ 


\ 












1 \ 


\ 






\ 




1 








\ 


\ 


\ 












\ 


\ 




\ 


\ 




1 












\ 




\\ 


1 u 




\ \ 


\ 


\ 


\ 


\ 


\ 




1 










\\ 


>^ 


4 






-'*f 


\^-fA 




I.I 


-w 


miA 


i\ 


0.7 


\a5 


\a35 


03. 


1^ 


sVv\^ 






C\ 


\ 


^ 


kH^ 


^1 


\ 




\\ 


\ 


L'- 


'-., 


6 


0.8 


1.0 


1.2 


1.4 ,.6-,ri 

AIR MASS (m 


2.0 

p' 


3.0 


4.0 


5.0 



Fig. 9. — Intensity of solar radiation on a horizontal surface 
(ly min~') as a function of air mass m,, and precipitable water 
vapor IV for a cloudless, dustless atmosphere. For elevated 
stations where pressure is p in millibars, multiply radiation by 
p/1013. Dashed lines represent extrapolated values. {After 
Fritz [31].) 

ground. Figure 9 shows the radiation on a horizontal 
surface during dust-free conditions, as a function of 
optical air mass and precipitable water-vapor content. 
The computations are based on Fig. 6 and a combina- 
tion of equations from Klein [31, 53]; it is assumed that 
half the scattered radiation reaches the ground. Much 
of the scattered radiation does reach the ground, but 
obviously this final result is only an approximation 
which agrees fairly well with observations and with 
other calculations. Summations over 24 hours (with the 
aid of Fig. 9) furnish daily totals which, when cor- 
rected by comparison with observations at several lo- 
cations, show the geographic and seasonal variation of 
cloudless-day radiation over large areas [31]. Such com- 
putations indicate that in the United States about 80 
per cent of the incident extraterrestrial energy reaches 
the ground during cloudless days. 

Some variations from average values are naturally 
to be expected. In cities particularly, one would expect 
marked average decreases of the order of about 20 per 
cent [40]. For snow-covered terrain, increased radiation 
will be measured because the strongly reflected radia- 
tion will be partially scattered back to the ground by 
the atmosphere. 

Transmission through Clouds. Clouds, however, will 
generally introduce the largest variations of the solar 
energy which reaches the ground. Haurwitz [43] has 
given the average solar energy transmitted to a hori- 
zontal sm-face through various types of clouds at Blue 
Hill, Massachusetts, and also the percentage of cloud- 
less-sky radiation transmitted. His data are shown in 
Fig. 10 and in Table VII. Large variations about these 



SOLAR RADIANT ENERGY 



29 



a\'erage values are of course to be expected for indi- 
vidual cases. 

The effect of snow in increasing the solar radiation 
will be particularly pronounced for overcast conditions 
because the energy which is reflected by the snow will 
be strongly reflected towards the ground by the base of 
the cloud. This is shown for visible radiation in Fig. 11 
[49]. For wider application the data of Table VII and 



90 



80 



70 



'tt: 60 

I 



50 



< 40 
o 



30 



20 



10 



\ 










., _ 






\ 
















\\ 
















\ 


K 


CLEA 

/ 


R 










\ 


N5 


/' 












^ 


^ 


\^Cs 


"•^ 










<^ 


^ 




"^ 














=^ 


.Sc ^ 




^ 


' ■ 




/ 

Ms 




06 


"^ 




=^ 
















1.0 



2.0 



AIR 



3.0 
MASS 



4.0 



5.0 



Fig. 10. — Solar radiation on- a horizontal surface through 
the types of clouds indicated. {After Haurwilz [43].) 



Table VII. Ratio of Solar Radiation with Overcast Skies 

TO Solar Radiation for Cloudless Skies 

(in per cent) 

{After Haurwilz [43]) 



Air mass 


Ci 


Cs 


Ac 


As 


Sc 


St 


;vi 


Fog 


1.1 


85 


84 


52 


41 


35 


25 


15 


17 


1.5 


84 


81 


51 


41 


34 


25 


17 


17 


2.0 


84 


78 


50 


41 


34 


25 


19 


17 


2.5 


83 


74 


49 


41 


33 


25 


21 


18 


3.0 


82 


71 


47 


41 


32 


24 


25 


18 


3.5 


81 


68 


46 


41 


31 


24 




18 


4.0 


80 


65 


45 


41 


31 






18 


4.5 










30 






19 


5.0 










29 






19 



will give average values of Q; here a and h are constants 
such that a + h = 1, S is the percentage of possible 
sunshine, and Qa is the value of Q when S = 100 (clear 
skies). This was really already assumed implicitly by 
Kimball in 1919 [51]. From examination of the radiation 
on individual days, average values of a have been 
found f or (S = and/or for c = 10 (overcast) by many 



40 



35 



30 



25 



20 



I 5 



< 

z 



M 



I 



Z 



y. 



z 



'/. 



t 



z 



SOLAR ALTITUDE 30° 



^ 



0- 



Ci 



Cc 



Sc 



Cb 



SI 



Nb 



SOLAR ALTITUDE 7° 



1 



V, 



Ci 



cc 



Sc 



Cb 



St 



Nb 



Fig. 11. — Diffuse visible skylight for different types of 
clouds (10/10 sky cover) above ground with snow cover 
(hatched bars) and without snow cover (clear bars) for solar 
altitudes of T and 30°. Dashed horizontal lines apply for clear 
skies. {After Kalitin [49].) 



Fig. 10 should be sepai'ated for conditions of snow- 
covered and snow-free ground. Also similar data should 
be computed foi- areas in which the climate is different 
from that of Blue Hill. 

Average Conditions. We turn now to the estimation 
of the average solar i-adiation Q which reaches the 
earth's horizontal surface on the average for all days. 
It is commonly assumed that 



Q = Qoia+ bS) 



(24) 



observers. Kimball found a 
D. C, and obtained 



0.22 for Washington, 



Q/Qo = (0.22 + 0.78S). 



(25) 



Ang.str6m found a = 0.235 for Stockholm; for annual 
values at Blue Hill, Haurwitz found a = 0.22 or 0.30, 
depending on the assumptions; Mosby obtained a = 
0.54 for the Arctic [42]. Recently several other authors 
have found values of a which vary considerably. Never- 



30 



RADIATION 



theless, when Q for average cloudiness conditions is 
desired, equation (25) is commonly used. 

In equation (24), a is usually determined from meas- 
urements of Q for individual days on which iS = and 
S = 100. Very few places have an average oi S = 
or S = 100 for a period of a month, and it is not cer- 
tain that equation (24) will yield average values of Q 
for periods which are made up of a mixture of clear, 
partly cloudy, and overcast days. A study of all suit- 
able data in the United States [33] in which only 
monthly mean values of Q and Qo were used gave the 
equation 



Q = Qo (0.35 + 0.61<S), 



(26) 



with a con-elation coefficient of -fO.SS between Q/Qo 
and S. Here Qo is the cloudless-day radiation. An ex- 
amination of the data (unpublished) revealed that in 
the western part of the country a was higher than in 
the eastern part. 

That a should vary is to be expected from Haur- 
witz's data (Fig. 10). The frequency of cloud types is 
not often available, but it can be seen that areas with 
greater frequencies of high clouds will have higher 
values of a than areas with high frequency of low clouds. 
Hence, the application of one equation such as equation 
(25) or (26) everywhere should be expected to lead to 
some inaccuracies even when the amoimt of cloudiness 
or of sunshine is known. Fortunately, for a considerable 
range of ;S, equation (25) or equation (26) will give very 
similar results for Q/Qq. Only in very cloudy or rela- 
tively clear areas will there be a difference in the result. 
For lack of more detailed information, Kimball applied 
equation (25) to the best cloud-amount data available 
to him and computed maps showing the distribution of 
radiation over the ocean area [52]. However, if the fre- 
quency of cloud types in some ocean areas is different 
from the average for the eastern United States, results 
different from those of Kimball should be expected. 

The computations from any of these formulas can 
approximate only long-term average values. At any 
one place and time large fluctuations from the normal 
value occur. For example, at Washington, the total 
radiation on a horizontal surface for a particular Febru- 
ary, say, may vary by as much as ± 20 per cent from 
the average for all Februaries and bear very little re- 
lation to S for that particular February. Angstrom 
[11] notes that in the short interval 1923-28 the annual 
total of radiation at Stockholm varied by ± 10 per 
cent from the mean for the six-year period. There is 
ample evidence therefore of large variations in the ra- 
diation that reaches the ground at particular points on 
the earth's surface. If the variations which Danjon 
found in the earth's albedo are verified, large fluctua- 
tions also occur in the total radiation that reaches the 
entire earth's surface in a period of a month or even of a 
year. Except for regions where clouds are rare, areas of 
JdcIow or above normal radiation (or surface heating) 
may occur anywhere, being influenced predominantly 
by the prevalence of the amount and type of clouds. 



GENERAL SPECULATION AND CONCLUSION 

From the thoughts implied or expressed earlier, we 
can extract a few for amplification and emphasis. 

Solar Radiation at the Ground. The solar energy Q 
absorbed by a unit area of the earth's surface is by far 
the largest portion of the absorbed energy. It is cus- 
tomary when discussing the average general circulation 
to consider that the greatest heating occurs at the 
equator where the air rises and that a whole chain of 
events takes place as a consequence. This equatorial 
heating is supposed to represent an average condition. 
Actually, even as an average condition, it is not a true 
picture for the simimer hemisphere. In the Northern 
Hemisphere summer, average Q is distributed rather 
uniformly with latitude, so that there is no pronounced 
maximum of radiation near any one latitude, and the 
maximum, such as it is, probably occurs near lat 40°N 
rather than at lower latitudes. The maximum surface 
temperatures occur in the middle of the large cloudless 
land masses, not necessarily at the equator. 

Let us speculate somewhat on the possible signifi- 
cance of the fairly unifonn surface heating in summer in 
middle latitudes. In the annual cycle of temperature it 
is well known that in inland areas the maximum of the 
average surface air temperature lags the maximum solar 
radiation bj' about four to eight weeks. Since advection 
in summer is generally small, the heat balance at the 
ground in situ may be an important factor in deter- 
mining the future average air temperature over a period 
of time such as a week or a month. In effect the ground 
acts as a heat reservoir; it gets hot to a considerable 
depth under the influence of the solar radiation which 
it receives, and it gives up its heat gradually to the 
atmosphere. 

The lag between the average surface air temperature 
and the solar radiation at the ground occurs in the mean 
or normal situation. What happens in any particular 
summertime week or month? As indicated earlier, the 
amount of solar radiation which reaches the ground in 
a period of a week or month may differ markedly from 
the normal value of solar radiation. Suppose the solar 
radiation received during a particular June is much 
higher than normal' Perhaps we can assume that the 
ground would get hotter (over and above its normal 
rate of heating) than it had been in the previous May 
and that the effect of the hotter ground would be to 
modify the air temperature towards higher temperature 
in the following July. 

Actually, we should of course examine the heat bal- 
ance at the ground and not the incoming solar energy 
alone. The solar energy is regularly measured in many 
places, and in the United States the network of such 
measurements is now nationwide. But the heat losses 
at the ground are not regularly measured as universally. 
In the face of such an observational deficiency, is it 
justifiable as a first approximation to assume that the 
variation of incoming solar energy in summer predomin- 
ates over other effects, such as variations in outgoing 
radiation? If this assumption is justified, and summer- 
time advection is not a predominant effect, an ano- 



SOLAR RADIANT ENERGY 



31 



maloiis solar energj' Q might influence the air tem- 
perature in inland areas with a lag in the same way 
as the normal surface air temperature lags the normal 
solar radiation. If such an effect could be found, the 
forecasting \-alue of the observed solar radiation would 
be obvious. 

Other studies involving the observed anomalous ra- 
diation may be profitable. The average annual cycle of 
atmospheric circulation is of course related to, if not 
entirely caused by, the change in the gradient of solar 
heating of the earth's surface. Here again perhaps study 
of the observed anomalous radiation distribution for a 
week or a month may reveal it to be a factor in the 
cause of large-scale weather changes. 

The Albedo of the Earth. To a certain extent the 
previous remarks concerning the significance of the dis- 
tribution of surface heating apply also to the heating 
of the entire planet. The planet-wide heating cannot be 
observed at present from surface observations. How- 
ever, by Danjon's technique the earth's albedo can be 
observed, although corroborating independent observa- 
tions are highly desirable. Furthermore, by making 
observations from several longitudes it may even be 
possible to estimate the longitudinal distribution of the 
albedo and therefore of the heating. The variations of 
these albedos from their average values may be related 
to the subsequent exchange of heat and of masses of the 
atmosphere between latitudes and between longitudes. 
Upper-Atmospheric Heating. The uncertainties re- 
garding the extent of heating in the ozone layer were 
discussed earlier and a quasi-practical experiment to 
determine the fluctuation of radiation during SID's was 
proposed. It is, of course, possible to attempt correla- 
tions of numerous solar parameters with meteorological 
parameters. The number, size, shape, and polarity of 
sun spots, as well as faculae, flocculi, prominences, and 
coronal lines are but a few of the parameters which 
have been or could be used. However, it seems to the 
author that if any relation does exist between solar 
variability and tropospheric meteorology over a period 
of a few daj's or longer, those solar parameters which 
are knoum to produce effects somewhere in the upper 
atmosphere would offer the greatest promise, and it 
would be better to seek correlations not with the solar 
variation itself but rather with the known terrestrial 
effect which has been produced. Prominent among such 
. solar-induced terrestrial effects are SID's and magnetic 
variations. 

The suggestion then is that we measure the variation 
of solar ultraviolet radiation which reaches the top of 
the ozone layer, and the variation of temperature there. 
Until such measurements are made we cannot be sure 
that solar variation is heating the ozone layer signifi- 
cantly above its normal temperature. After the magni- 
tude of ozone heating has been established, correlations 
of tropospheric effects with solar parameters which 
produce the ozone heating would ob\'iously be indi- 
cated. In the meantime, the SID seems to be a par- 
ameter which is likely to be related to abnormal ozone 
heating; as such it may be related to surface pressure 
changes. 



Absorption by Clouds. Since some of the measure- 
ments suggest large absorption of solar energy by 
clouds, it would be desirable to investigate the absorp- 
tion further. This can be done from airplanes, as de- 
scribed earlier; but it may also be feasible to investigate 
the absorption from the ground. This might be ac- 
complished by spectroscopic measurements on clouds 
from X = 0.5 M to X = 2.5 n. On the basis of the data of 
Fig. 1 and our knowledge of the spectral distribution 
of clear-sky light [55], we can approximate the spectral 
distribution of the solar energy which irradiates the 
tops of clouds. Furthermore, Fig. 7 shows the extinc- 
tion of parallel light by droplets in the absence of ab- 
sorption, and shows that if the droplets are large (2:rr/X 
> 50), Ks becomes nearly independent of X for the 
spectral region between 0.5 fi and 2.5 fj.. This ought to 
be true also for diffuse radiation such as that produced 
by clouds. At 0.5 /x the absorption coefficient of liquid 
water is in reality very small, so that the ex-tinction by 
clouds at 0.5 n is caused wholly by scattering. Conse- 
quently /o.5, the measure of spectral intensity at 0.5 m, 
can serve as a standard against which to compare the 
spectral intensities at longer wave lengths such as 2.0 m- 

From Fig. 7, together with some reasonable assump- 
tion about the droplet sizes in the cloud and the relative 
spectral irradiation of the cloud top, we can calculate 
/2.0 relative to /0.5 on the assiunption that no absorp- 
tion is present. The difference between the calculated 
/2.0 and the observed /2.0 might serve as a first approx- 
imation to the absorption. Greater refinement can prob- 
ably be obtained from Mecke's theoretical discussions 
[59]. 

Conclusion. We have discussed the state of our knowl- 
edge in the field of solar radiation and speculated about 
some of the deficiencies in that knowledge and in its 
application to meteorology. On the question of the solar 
energy potentially a^'ailable for "use," the suggestions 
(1) that the albedo (35 per cent) of the earth is smaller 
than the value (43 per cent) which has often been ac- 
cepted, and (2) that the absorption by clouds is higher 
than formerly assumed may require a re-evaluation of 
the disposition of the radiation received by the earth 
in the mean. That the long-term average radiative bal- 
ance controls the average weather pattern is, of course, 
not subject to question. The excess or deficit of ab- 
sorbed solar radiation by comparison with the normal 
absorbed radiation should also significantly influence 
the weather elements averaged over relatively short 
periods. Whether a week, a month, a season, or longer 
is the required "relatively short period" remains to be 
investigated. 

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An attempt has been made to limit the number of references. 
Manj^ of those listed here contain additional useful ones. A 
relatively large number of references are contained in several 
of the items listed below; these have been marked with an 
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32 



RADIATION 



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7. Aldrich, L. B., "The Reflecting Power of Clouds." 

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46. Houghton, H. G., and Chalker, W. R., "The Scattering 

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49. Kalitin, N. N., "Einfluss der Bewolkung auf die Hellig- 



SOLAR RADIANT ENERGY 



33 



keit der Erdoberflache durch diffuses Licht der At- 
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Solar Heat Load on Man." /. Meteor., 5:119-129 (1948). 
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Planets. Chicago, Universitj^ of Chicago Press, 1949. 
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Berlin, Gebr. Borntraeger, 1942, 1943. 
*56. List, R. J., ed., Smithsonian Meteorological Tables, 6th 

ed. Washington, Smithson. Instn. (in press). 

57. LuCKiESH, M., "Aerial Photometry." Astrophys. J., 

49:108-130 (1919). 

58. Marvin, C. F., "On the Question of Day-to-Day Fluctua- 

tions in the Derived Values of the Solar Constant." 
Mon. Wea. Rev. Wash., 53:285-303 (1925). 

59. Mecke, R., "Die Gesetze der Liohtausbreitung in optisoh 

triiben Medien und das Sichtweiteproblem." Meteor. 
Z., 61:195-199 (1944). 

60. Menzel, D. H., "Earth-Sun Relationships" in "Cen- 

tennial Symposia, Dec. 1946." Harv. Obs. Monogr., No. 
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61. Milankovitch, M., Phenomenes Thermiques. Paris, 

Gauthier-Viliars et Cie, 1920. (See also "Mathematische 
'Klimalehre und astronomische Theorie der Klima- 
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und R. Geiger, Hsgbr., Band I, Teil A. Berlin, Gebr. 
Borntraeger, 1930.) 
*62. MiTRA, S. K., The Upper Atmosphere. Calcutta, The 
Royal Asiatic Society of Bengal, 1948. 

63. Moon, P., "Proposed Standard Solar-Radiation Curves 

for Engineering Use." J. Franklin Inst., 230:583-617 
(1940) . 

64. National Bureau of Standards, Ionospheric Radio 

Propagation. Nat. Bur. Stand. Circ. 462, Washington, 
D.C.,1948. 



65. Neiburger, M., "The Reflection of Diffuse Radiation by 

the Sea Surface." Trans. Amer. geophys. Un., 29:647- 
652 (1948). 

66. "Reflection , Absorption and Transmission of Insola- 
tion by Stratus Clouds." J. Meteor., 6:98-104 (1949). 

67. Paranjpe, M. M., "The Variations of the Solar Constant 

and Their Relation to Weather." Quart. J. R. meteor. 
Soc, 64:459-476 (1938). 

68. Pettit, E., "Measurements of Ultraviolet Solar Radia- 

tion." Astrophys. J., 75:185-221 (1932). 

69. Phillips, M. L., "The Ionosphere as a Measure of Solar 

Activity." Terr. Magn. atmos. Elect., 52:321-332 (1947). 

70. Ramanathan, K. R., and Karandikab, R. V., "Effect 

of Dust and Haze on Measurements of Atmospheric 
Ozone Made with Dobson's Spectrophotometer." Quart. 
J. R. meteor. Soc, 75:257-267 (1949). 

71. RossBT, C.-G., "The Scientific Basis of Modern Meteorol- 

ogy" in Handbook of Meteorology, F. A. Berry, E. 
BoLLAT, and N. R. Beers, ed., pp. 502-529. New York, 
McGraw, 1945. 

72. Stair, R., "Measurement of Ozone over the Organ Moun- 

tains, New Mexico." /. Res. nat. Bur. Stand., 40:9-19 
(1948). 

73. Sterne, T. E., "On Periodicities in Measures of the Solar 
nat. Acad. Sci., Wash., 25:559-564 



74. 



Sterne, T. E. 

Constant." Proc. 

(1939). 
Tanck, H.-J., 



"Die tagliche Erwarmuug der Atmosphare 
infolge der Absorption der direkten Sonnenstrahlung 
durch den atmospharischen Wasserdampf." Ann. Hy- 
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Flight of 1935 in the Balloon "Explorer II." Nat. Geogr. 
Soc, Washington, D. C, 1936. (See pp. 133-138) 
*76. van de Hulst, H. C, "Scattering in the Atmospheres of 
the Earth and the Planets." (In [54], pp. 49-111.) 

Waldmeib, M., Ergebnisse und Probleme der Sonnenfor- 
schiing. Leipzig, Becker & Erler, 1941. 

Wexler, H., "A Comparison of the Linke and Angstrom 
Measures of Atmospheric Turbidity and Their Applica- 
tion to North American Air Masses." Trans. Amer. 
geophys. Un., 14th Annual Meeting, pp. 91-99 (1933). 

WuLF, O. R., and Deming, L. S., "On the Production of 
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atmos. Elect., 43:283-298 (1938). 



77. 



78. 



79. 



LONG-WAVE RADIATION* 

By FRITZ MOLLER 
Gutenberg University at Mainz 



Introduction 

Long-wave radiation occupies a peculiar position in 
the science of meteorology in that its effects in the free 
atmosphere are known only through theoretical cal- 
culations and not through measurements. These calcula- 
tions are, nevertheless, based on experiments in the 
laboratory and in the atmosphere. The atmospheric 
radiation is very seldom measured from balloons [3] 
or from aircraft [17], but quite frequently on the ground 
where the radiation from above is observed. It appears 
that part of the measurements from airplanes are in 
error; and the measurements on the ground have seldom 
found an evaluation that went beyond the formulation 
of empirical equations to approximate their average 
values. The theoretical deductions concerning the radia- 
tion in the atmosphere are much more extensive, and 
it would be most desirable to support them by careful 
measurements, especially since the experimental tools 
are available. 

Initially, much was expected from the investigations 
of long-wave radiation in the free atmosphere. It was 
hoped that they would furnish an explanation for the 
latitudinal differences in the temperature and altitude 
of the tropopause, an interpretation of the variations 
of these values from day to day, and a physical elucida- 
tion of the origin of the inversions in the free atmos- 
phere. In all these problems the solutions at times 
seemed to be near at hand, but then they receded. It 
appears to the author that today the emphasis of 
research is directed more toward the investigation of 
the radiative balance and heat budget in the atmos- 
phere. 

In the following, the techniques of measurement are 
omitted and little will be said concerning the mathe- 
matical-physical basis of the calculations, since two 
detailed treatises which are still up to date ai-e available 
[14, 28]. They cover these subjects very thoroughly. 
On the other hand, we shall discuss in great detail the 
number of instances where long-wave radiation is in- 
volved in the problems of general meteorology. 

Long-wave radiation is a heat radiation; its energy 
is derived from the kinetic energy of the molecules. 
The radiators of this energy are those atmospheric 
gases that have absorption bands in the temperature 
radiation range of 4 to approximately 100 n, that is, 
water vapor, carbon dioxide, and ozone. The effect of 
the water vapor is restricted almost exclusively to the 
troposphere, in which carbon dioxide and ozone are 
of little significance. The latter two gases become of 
great importance in the stratosphere between 15 and 
35 km. In addition, heat is radiated by the ground and 
the clouds. 



■ Translated from the original German. 



The Absorption Laws 

From the beginning, the theoretical calculations were 
set up in such general terms that it became possible to 
investigate the radiation properties of any atmosphere 
with any temperature distribution and any possible 
arrangement of radiating and absorbing media. This 
was done by the development of special radiation dia- 
grams or radiation charts. This approach was justified 
by two facts: (1) The intensity of the radiation which 
is emitted by an element for a given wave length is 
proportional to the black-body radiation and is thus 
a function only of the absohite temperature; (2) this 
radiation is proportional to the mass of the radiating 
medium, which means, in the troposphere, to the 
amount of water vapor. It is of particular importance 
that the proportionality constant, that is, the absorp- 
tion coefficient k, is really a constant in its first ap- 
proximation and not a function of any other quantities. 
However, in reality such a dependence of k on the air 
pressure and on the temperature does exist and gives 
rise to particular difficulties in advanced investigations. 

It should immediately be pointed out that the con- 
struction and application of radiation diagrams become 
impossible if there exist in the atmosphere two different 
media whose masses in a given volume element vary 
independently of each other from case to case, but 
whose emissive power at the same wave length is of 
the same order of magnitude so that the effect of the 
one medium cannot be neglected as compared to that 
of the other. Such conditions prevail in the stratosphere, 
for instance in the case of ozone and carbon dioxide. 
It is possible to consider two media in the same space 
element of the atmosphere only when one of the radia- 
tors is a gray radiator, that is, when its absorption 
coefficient k is the same for all wave lengths [31]. 

Parallel Radiation. If an absorbing medium m is 
penetrated by a beam of parallel rays, absorption takes 
place according to an exponential law. The emergent 
radiation I\ is 

Ix = /oxe-*^-, (1) 

where the subscript X indicates monochromatic radia- 
tion, and Jc is the incident radiation. The absorbed 
portion is 

A = (7o - 7)//o = 1 - e-*x-. (2) 

The length of the path which the radiation follows in 
penetrating m does not appear in this equation. This 
means that the absorption is only a function of the 
penetrated mass m, or that the absorption coefficient 
k\ is independent of the density of m throughout the 
penetrated cylinder. If Jo is black-body radiation at a 
temperature T, whose value is given by Planck's law, 

7o = &(\, T) dw, 



34 



LONG-WAVE' RADIATION 



35 



(where dw is the soHd angle), and if the mass tn has the 
same temperature 1\ then m radiates, according to 
Kirchhoff's law, the same amount of energy as it ab- 
sorbs; that is, it emits 

E = (S(X, T)do:-A = &{\, T) dw (1 - e-*x"0. (3) 

A mass element dm of temperature T therefore sends 
through the absorbing mass m the radiation 

dE = g(X, T) dco-dA = (S(X, T) do> ■ e-'^-x™fcxrfm. (4) 

If the mass element has a diffei'ent temperature T\, 
the radiation is simply 



to(X, Ti) di^-e-^^'^kxdm 



(5) 



in which it is assumed that k\ is not a function of the 
temperature of the mass m. 

Diffuse Radiation. The simple basic law represented 
by equations (3) and (4) holds essentially for all com- 
plications that appear in the atmosphere. First of all 
we must take into consideration the fact that the radia- 
tion is not parallel. Let us consider the radiation of a 
layer of air of infinite horizontal extent which is part 
of a uniformly stratified air mass and which is to con- 
tain the radiating mass dm, over an area of one square 
centimeter. Then the radiation emitted from this mass 
will arrive on a receiving surface at all angles of inci- 
dence 0°< (p <90°. The integration of equation (4) 
over <p can be reduced to known functions and the 
radiation of the layer element is 



dS = Trg (X, T) 2mkxm) kxdm. 



(6) 



The radiation of a layer of finite thickness with a tem- 
perature T is then 

S = ttS (X, T) [1 - 2Hs(kxm)]. (7) 

The functions Hn and H^ (called -Eis and Eii by Elsasser) 
are tabulated [27], so that they can be used for exact 
calculations. The expression A'' = [1 — 2i?3 (kxm)] 
can be considered as an absorption function of diffuse 
radiation, and its differential is accordingly 

dA'' = 2Hi{k\m) kxdm. 

Within a large range the following approximations can 
be made: 

2H2{x) ^ LGGe-i-ss^ and 2H2{x) ;^ e-i-^"^, 

which means that the laws for diffuse radiation between 
atmospheric layers are replaced by the laws for parallel 
radiation in which, however, the absorption coefficient 
is multiplied by % . 

Radiation from a Spectral Line. A further modifica- 
tion of the simple absorption laws is required by the 
physical processes that take place when gas masses 
radiate. The absorption bands of the multimolecular 
gases are not continuous, but are resolved into numer- 
ous closely spaced absorption lines. The absorption 
coefficient is extremely high in the center of each of 
these lines, while it is smaller by about two orders of 
magnitude between two lines. Thus, even if we consider 
only a very small spectral band AX which contains only 
a single line, we must take into consideration a varia- 



tion of k\ at a ratio of 1 : 100. This is most easily done 
by determining once and for all the absorption function 
of a line. The form of a spectral line, that is, the law of 
the decrease of the absorption coefficient from the 
center towards the edges, is known as the dispersion 
form: 

koS'/A 



fCp — 



{u - voy + 5V4 



(8) 



(Instead of X, the frequency v = 1/X cm~^ is used; 
5 is also given in cm~^) The significant values in this 
law are (1) the absorption coefficient m the center fco, 
(2) the half-value width 8 of the line, and (3) the dis- 
tance between two adjacent fines Ac. The ratio 8/Av 
determines to what fraction of fco the absorption coeffi- 
cient k decreases between two lines. Neither d nor Av 
has the same value in one band, let alone in different 
bands, of the same spectrum. The distance between 
lines Av varies irregularly, because of the overlapping 
of differing laws for the various spectral lines. Only 
very few values have been determined for 6, because 
the measurements are extremely difficult to make. 
Therefore, it is usually assumed that 3, as well as Av, 
is constant for the entire spectrum. Although this as- 
sumption is only an expedient, there is no possibility 
of a more exact evaluation at the present time. 

If we integrate the absorption laws for parallel or 
diffuse radiation over such a dispersion form of a 
spectral line, we arrive at new laws, that is, new absorp- 
tion functions, Avhich can be expressed by 



L {kom) 



+A>./2 



-j /.-1-ac 
Av J-Avl 



1 - 2H. 



kf,mb /4 



{v - v,Y + 5-/4/ J 



dv (9) 



for the radiating layer m, and by 



I/(kom) 
Av J- 



+Ai,/2 p 



A„/2 



1 — exp 



komb /4 



{v - v,y- + 5V4, 



dv (10) 



for the radiating column. As before, the radiation of a 
layer element is the first derivative of this function with 

respect to m, that is, dtn for parallel or diffuse 

radiation. It is of no consequence whether this integral 
can be solved analytically or numerically. If it can be 
tabulated, it can be used for any further calculations. 
The two new equations, (9) and (10), contain as a 
parameter the ratio between the half-value width and 
the distance between lines, a — Av/h. 

An approximate solution for L maj^ be obtained, if 
we assume 5-/4 in the denominator to be negligible 
compared to {y — vo)'-. In that case 

L {ku7n) ^ y/koTrm/a^. 

This indicates that the radiation of a gas layer of 
finite thickness m is proportional to the square root of 
m if the absorption occurs in individual lines. If, on 
the other hand, we were dealing with continuous absorp- 
tion, we would arrive at an exponential function. Thus, 



36 



RADIATION 



simpl,y by plotting experimental absorption values 
against the square roots of m, or by the usual repre- 
sentation of In (1 — A), we can determine whether we 
are dealing with a continuous distribution of the absorp- 
tion coefficient, or with a resolution into individual 
lines. It is important to reahze that this method is 
applicable even if the apparatus is not sufficiently 
sensitive to resolve the individual lines. Strong [48] 
applied this method to entire bands whose separate 
lines may have very different values for fco.' 

Radiation Diagrams 

The knowledge of the absorption of a spectral line 
gives us one basis for the calculation of atmospheric 
heat radiation. The second basis is the distribution of 
the \'alues for ko over the various wave lengths. For 
water vapor, which is most effective in the troposphere, 
the available measurements have been tabulated by 
Elsasser [14] and Moller [34]. Callendar and Cwilong 
give analogous figures. The absorption shows very great 
differences. In the rotation spectrum, ko is of the order 
of 10^ cm^ g-'; in the rotation-oscillation spectrum at 
6 /J it is about 10' cm- g-^; whereas it decreases in the 
"window" of the water vapor to 1 cm- g-' or below. In 
spite of these large differences we can never neglect one 
spectral range as compared to another, because the in- 
tensive radiation in the range of large values of ko is 
readily absorbed even by very thin layers, whereas the 
low radiation intensities at small values of ko are scarcely 
absorbed. However, thick and distant layers can parti- 
cipate in the emission of this radiation. Therefore we 
need the cumulative effect of all wave lengths for com- 
parison with measurements. Miigge and Moller [37] 
were the first to use a graphical method in which the 
integration over all wave lengths is computed in ad- 
vance and represented in diagrammatic form. Elsasser 
[14] developed a similar diagram, which is the same in 
principle, but which differs somewhat in arrangement. 

According to the foregoing discussion, the radiation 
at wave length X of a thin layer of gas of temperature 
T is given by 



dS, = xSCX, T) ^J4^ dm. 



dm 



(11) 



where ko varies from line to line. Even larger spectral 
ranges that comprise a number of lines can be com- 
bined as long as ko varies less than /o, in the range of 
one line, that is, less than 100:1. Then the total radia- 
tion of a layer element dm is obtained by summation 
over all wave lengths. 



.dS = rdm E HK T) ^^ii^ AX, 
X dm 



(12) 



1. (Note added July, 1950.) Callendar [11] used an empirical 
absorption law L{w) = w/(w + xlh) in which wo is a constant 
characterizing the degree of absorption; this law is easily 
applicable in theoretical investigations and covers the observa- 
tions well. Using all experimental data of water vapor, Cwilong 
[12] recently deduced an empirical absorption function, but he 
gives numerical values only and not an analytic expression. 
The values of the function are available for narrow frequency 
intervals of the whole long-wave water-vapor spectrum. 



and the radiation of a layer m of finite thickness upon a 
surface element situated in the one boundary surface 
of the layer m becomes 

S = . f dmY. &{\ T) ^J^p^ AX. (13) 
Jo X dm 

This is the radiation of an atmospheric layer upon a 
unit area, for instance the radiation of the entire atmos- 
phere upon the unit area of the sensitive surface of a 
measuring instrument placed on the ground. The inte- 
gration over 771 is difficult at first, because the tempera- 
ture T is in general not constant but a function of m, 
that is, a function of the radiating mass situated be- 
tween an altitude above ground and the surface of the 
earth. If we consider an isothermal atmosphere of 
temperature To, then 



.Sr„ = 7r / dm X) <§(X, To) 
Jo X 



dL^ikom) 
dm 



AX = XtoM (13a) 



will be a function X of m. If we now plot the absorption 

1.0 .8 .6 .4 .2 





.05 .1 


.2 




.5 


1 


2 00 


.05 .1 


.2 




.5 


1 


2 00 


G.OI .05 .1 


.2 




.5 


1 2 


5 00 


.01 .05 


.1 


2 


.5 1 


2 


5 10 CO 



.4 



.6 



1.0 



Fig. 1. — Absorption functions. The linear scale at the top 
gives the transmitted radiation. The linear scale at the bottom 
gives the absorptive or emissive power. Numbers on the func- 
tion scales from A to D are the absorbing mass m. 

(A) 1 -€-'■■"• for k = 1.66. Parallel radiation. 

(B) 1 -2 Hz(m). Diffuse radiation. 

(C) L'^a - 5.5 (ko>n) for ka = 6.5. Diffuse radiation of a 
spectral line with a = 5.5. 

(D) L'^a . 12 (kom) for ko = 20. Diffuse radiation of a spec- 
tral line with a = 12. 

The values of k and ki, are chosen so that for the same mass 
m the absorption will be 0.5 in each case. 

function X as the abscissa and provide it with a scale of 
m, as in Fig. 1, we can read at the scale division m, the 
radiation intensity emitted by the isothermal layer of 
temperature To- However, X also indicates the amount 
absorbed by this layer when an infinite surface of 
temperature To transmits black-bodj^ radiation through 
this layer. If fco does not vanish for any wave length, 
an infinitely thick layer (?re = oo) will have total 
absorption. Accordingly, the radiation emitted by an 
infinitely thick layer of gas is equal to the black-body 
radiation: the point m = <» of the scale lies at X = 
<yTo\ 

It can be seen immediately that the radiation of a 
layer element dm of temperatiu'e To is also given by the 
differential of X: 



dS 



dm 



Xt„(to) dm. 



In order to find the radiation of a layer element of a 
temperature other than To, a new evaluation of the 



LONG-WAVE RADIATION 



37 



summation over X in (12) or (13) with T as a parameter 
becomes necessary. Let the ratio of the radiation of 
the two layer elements be y; then 



y{T, To, m) = 



Z to(X, T) f- L'(fcom)AX 
X dm 

E S(X, To) ^ L''{kom)A\ 
\ dm 



(14) 



We are now able to determine the radiation of the 
layer element dm of temperature T from the product 

d 



dSr = y {T, To,m)^Xr„{m) dm. 
dm 



(15) 



From (15) follows the key equation of the radiation 
diagram 



S = / y(T, To, m) dXroM, 
Jo 



(16) 



where T may now be any function of m, that may be 
given by observation or assumption. If we now plot y 
on the ordinate against X on the abscissa, we obtain a 
graph with curves for every value of T, in which y = 
1 signifies that T = To, and T < To gives values of y 
less than 1 (Fig. 2a). The radiation of an isothermal 



40° 


COg 


r ^° 1 
















^ 


~^0°-- 
^80°- 


^^ 


1 10 ^CALCtvT 


2mIN"I 


0° 


I 


^ 








/ 






\ 






-^ 




1 






-80° 




"~^ 


— 










_~~ 











10 



10 



10 



00 



Fig. 2o. — Radiation diagram according to Moller. The heavy 
lines refer to dovvncoming radiation of the atmosphere at the 
ground (I), the radiation at 7 km received from below (II), 
and the radiation at 7 km received from above (III). 

atmospheric layer is then given by the area bounded 
laterally by parallels to the y-axis through m = and 
m = m, by the X-axis at the bottom, and the line T 
at the top. The radiation of a nonisotherma atmos- 
pheric layer in which 7" is a function of m can be found 
by plotting the temperature distribution T(m) in the 
network of curves for m and T, and integrating. This is 
the basic principle of all radiation diagrams. Aside from 
the use of different absorption values, /co, Elsasser's 
chart is an authalic transformation of this principle, 
in which the isotherms are made rectilinear, and, as 
a result, the lines of equal m-values become curved. 
The curvature is hardly noticeable, because the lines 
for m = and m = » , which, as the boundaries of the 
graph, remain straight lines, intersect at the point 
T = 0. Thus the diagram assumes triangular or trape- 
zoidal shape (Fig. 2b). Furthermore, abscissa and ordi- 



nate are interchanged by comparison with Moller's 
diagram. 




40° 
Fig. 26.- 



-Radiation chart according to Elsasser. The heavy- 
lines correspond to those in Fig. 2a. 



Even though the principle of the two radiation dia- 
grams is the same, there are certain numerical differ- 
ences. These are best illustrated by a comparison of 
the functions X40C and X_8oc in the two charts. The 
values T = -|-40C and -80C are the highest and 
lowest temperatures shown. Table I shows that there 

Table I. Radiation or an Isothermal Layer with a 

Water-Vapor Content w in Per Cent of a-T^ as 

Given by Elsasser (E) and Moller (M) 





w (g cm-=) 


Temperature 


0(CO'. 
only' 


10-= 


10-2 


lo-i 


1 


10 


„ 




% 


% 


% 


% 


% 


% 


% 


+40C {E 


17.0 
13.3 


26.8 
24.4 


41.1 
41.5 


57.8 
58.3 


75.9 
72.7 


91.9 
89.0 


100.0 
100.0 


-80C {E 


16.6 
13.1 


38.1 
32.7 


58.0 
56.4 


76.1 
75.0 


88.8 
85.2 


96.6 
93.3 


100.0 
100.0 



is good agreement with differences of less than 1 per 
cent in the middle range of amounts of water vapor 
between 3 X 10"' and 3 X 10"' g cm-=. In the range of 
smaller or larger amounts of water vapor M5ller's 
values are about 2 per cent lower than Elsasser's. (The 
first edition of Elsasser's chart, as well as the earlier 
edition of the chart by Miigge and Moller both showed 
radiation values 10 to 15 per cent lower in the middle 
range of water-\-apor amounts. The agreement of the 
revisions made by both authors independently during 
the war is rather remarkable.) 

There is more of a difference in the evaluation by the 
two authors of the radiation of carbon dioxide. For the 
amount of CO-2 normally present in the atmosphere, 
there is almost complete absorption in the extraordi- 
narily intense band around 14.9 m even by only very 
thin layers. The weak extreme boundaries of the ])and 
extend to 12.5 m and 17.5 n, respectively. Elsasser now 



38 



RADIATION 



assumes that in the region from 13.1 jj. to 16.9 m the 
CO2 ahvays absorbs so strongly that we can assume 
total absorption, and that therefore the radiation 
emitted in that range by an atmospheric layer is equal 
to the black-body radiation at a temperature existing 
at the surface of such a layer. Moller [35] assumes a 
width of only 3 m for this range, that is, from 13.5 to 
16.5 Mj and estimates that within these wave lengths 
the absorption by water vapor is equal to that by 
CO2 only when the specific humidity is 100 g kg~^ or 
more. Outside of these boundaries, however, the ab- 
sorption by H1O is greater than that by CO-2. Accord- 
ingly, the C0-> absorption at 273K is 18.4 per cent 
according to Elsasser and 14.6 per cent according to 
Moller. In addition, Moller gives a scale in his chart 
which permits determination of the radiation effect of 
CO9 for large temperature variations at low altitude 
(close to the ground) or for very low CO2 content of the 
air (stratosphere). 

Another point of comparison consists of the numerical 
values assigned to the absorption coefficient /co by 
Elsasser and by Moller. In the 6-/i band MoUer's values 
are somewhat higher. The same applies to the absorp- 
tion increase from 10 y. to the rotation band, while in 
the core of this band the values are lower. Elsasser 
first calculated his graph with the coefRcients of his 
table. Later, however, he corrected it according to 
measurements of total absorption and concluded from 
these measurements that the /co values around 6 /x 
were originally too low, while those for 50 ti were too 
high. This makes the agreement of the fco values even 
better than a comparison of the numerical values would 
indicate. 

Lately, an important objection has been raised 
against both radiation diagrams. The absorption func- 
tions for a spectral line, L''{kom), which are used by 
both authors, contain the assumption that a = Av/S = 
5.6, wherein S was set at 0.5 cm~' and the distance 
between lines, Av, was assumed to be 2.8 cm~' as the 
mean of the range investigated by Eandall and his 
collaborators. According to recent measurements by 
Adel [1] on two lines near 16 and 18.6 ;u, it was found 
that 8 = 0.23 cm-^; from this it follows that a = 12. 
The absorption function for a line L'' is also shown in 
Fig. 1 for a = 12. The author suspects that the applica- 
tion of the new function will not lead to any important 
differences from the previous radiation charts, since 
the differences of ko at 10 n, as compared to those at 
6 n and 50 n, are so large as to render all refinements 
negligible. 

The Downcoming Radiation of the Atmosphere 

The simplest possible application of the radiation 
charts arises in the calculation of the do'micoming 
radiation R of the atmosphere and of the effective 
nocturnal radiation E = aTo* — R of the ground. 
Only a few direct comparisons of the measured and the 
calculated values are available. 

Wexler [50] compared measurements made in Alaska 
and North America under winter conditions with radia- 
tion values calculated from Elsasser's diagrams and 



found that on the average the calculated outgoing 
radiation values were about 0.035 cal cm~^ min~^ higher 
than the observed values. This deviation, for which 
Wexler has no explanation, must probably be ascribed 
to the use of the earlier edition of Elsasser's diagram 
which, in the range of water-vapor content in ques- 
tion, furnishes a value for downcoming radiation ap- 
proximately 10 per cent lower than the later edition 
of this chart. 

F. A. Brooks [7] and Robinson [43] carried out com- 
parative calculations for some cases of their numerous 
observations, but used them essentially to compute a 
radiation diagram on an empirical basis (see p. 40). 
However, in part of these observations in the free 
atmosphere only the total water-vapor content was 
used. So far, in most cases, no aerological measurements 
were made concurrently with the radiation measure- 



.7 



- 


__ — — 






" 














^-^^ 








/ ^r--r^r\ \ \ \\ ^ 






\\v 


W 




** --<-^\ \ \ \ \ \ \ \ 


WW 


\\\ 


: 


^ ^-^xVWWWWn 


WW 


,w,\ 


/ .x'aX \ \ \ \ \-j*A-VV\ 

/ .^\\ xX^-vtaa \ \ \ \ 
/ ^ka \ \ X-Vax \ \ \ \ \ \ \ 


\\\V 


\\\^ 




/ -A \ \ V><A^\ \\\\\\\\\ 


WW 


Wv 




/ •<\ \ \<A \ \ \ \ \ \\^--^--*-^""^ 








/ /\VC\\\>'''^ 






- 


/ XY\\ v^^ 












/\/\ \/ ^^ "^ 






" 


v\ / ^ 








X y y 






~ 


/v ^ 






~ 


/ / 








/ 
1/ 1 1 I 1 1 1 1 1 


1 


1 





4 8 12 16 


20 


24 



e (MB) 
Fig. 3. — Scattering of the relative atmospheric radiation 
R/a-T-' according to Bolz and Falckenberg 16]. Seventy per cent 
of all measured values lie in the hatched region, and 
ninety -eight per cent of all values lie within the region bounded 
by the dashed line. 

ments. Therefore only the variables measured on the 
ground such as pressure, temperature, vapor pressure, 
and cloudiness were used to organize the measurements 
and to develop interpolation formulas. The best known 
are those by Angstrom and Brunt which give the 
ratio R/aTo'' as a function of the vapor pressure at 
ground level only where To is the air temperature at 
the point of observation. Numerous authors have 
derived the constants of this formula from their meas- 
urements, but the scattering of the constants given by 
the different authors is as great as the scattering of the 
individual measurements around the curves plotted by 
each author [28]. Only recently Bolz and Falckenberg 
[6] gave constants for Angstrom's formula which re- 
sult in values for the downcoming atmospheric radia- 
tion which are 7 per cent higher than the constants so 
far assumed as best values (Fig. 3). 

If we assume a relative humidity that does not vary 
with height and a normal lapse rate of 6C km~^, we 
obtain the values for R (at To = 283K) given in Table 
II, according to Moller. These figures are higher than 



LONG-WAVE RADIATION 



39 



comparative values [28] that can be calculated ac- 
cording to 

R^ = aTo* (0.79 - 0.174 X IQ-"-""'") (Angstrom) 
R^ = o-ro" (0.48 -f 0.60 V7o). (Brunt) 

Three influences inay cause the discrepancies and 
also the large scattering of individual measurements 
around the interpolation formulas. They are (1) the 
consideration of temperature, which is all too inac- 
curate, (2) the neglect of ground inversions, and (3) the 
additional effect of absorbers other than H2O and CO2. 
These three influences will now be considered in turn. 

1. The formulas of Angstrom and Brunt give the 
radiation of the atmosphere as proportional to To^. 
This law is taken into account in Holler's diagram by 
the fact that the area under a given isotherm T, which 
represents the radiation of an isothermal atmosphere 
with w = 00 and C02-content = 00 , is equal to the 
black-body radiation aT*. An isothermal atmosphere 
of OC with the limited vapor content 3 g cm^^ has a 
radiative power R = 0.826 aTo^; a layer of equal con- 
tent at +40C gives R/aTo^ = 0.804 and at -40C, 
R/aTo* = 0.866. The variation of this factor, frequently 

Table II. Calculated Downcoming Radiation R 

AND Efjective Tebrestbial Radiation E 

(For To = +10C, ground -level vapor pressure co, and 

total water-vapor content W) 



CO (mb) 

W (g cm-2) ..._.._..... 
R (oal cm ^ min 1) . . . 
E (cal cm~^ min-i) . . . 
E/aTl (per cent) 



1.23 


3.7 


6.1 


8.6 


17.3 


0.224 


0.67 


1.12 


1.56 


2.24 


0.334 


0.369 


0.3S5 


0.396 


0.408 


0.196 


0.161 


0.145 


0.134 


0.122 


37 30 


27 


25 


23 



20.0 
3.64 
0.425 
0.105 

20 



called emissivity, is caused by the changes of the 
ordinates of the T-lines in the diagram with w. The 
variation may also be expressed by the assumption 
that the radiation of such a limited vapor mass in- 
creases more slowly with T than with T^ Accordingly, 
it appears that we can set 

R/aTo'^ = C[1- yiTo - 273)], 

in which To = observed temperature near the earth's 
surface, and 

C = {R/(tT^^)t„ = 273 

is a function of the water content W of the atmosphere. 



W g cm ^ 
y 10-' deg-i 



0.2 


0.5 


1 


2 


3 


-2.0 


1.0 


4.0 


7.0 


8.5 



4 
9.5 



tion measurements are made there exists a ground 
inversion, the magnitude and temperature of which are 
usually unknown. However, the layers next to the 
ground also furnish a considerable portion of radiation 
from above. (The values in parentheses in the following 
statement are percentages of the black-body radiation.) 
According to an estimate by Moller [28] for a normal 
atmosphere, 37 (28) per cent of the radiation proceeds 
from the layer 0-10 m, 71 (53) per cent from 0-100 m, 
and 88 (66) per cent from 0-500 m. Accordingly the 
effect of a ground inversion is great; an attempt at 
estimating this effect is shown in Table III. The down- 
coming atmospheric radiation R and the effective ter- 
restrial radiation E are given for an atmosphere of 
To = 273K and W = 1.12 g cm-^. 

This table indicates that a ground inversion can 
reduce the effective terrestrial radiation to ^ its nor- 
mal value, and under the extreme conditions found by 
Mosby during the polar night, to as low as }i. There- 
fore, any comparison between calculation and observa- 
tion becomes impossible if the vertical temperature 

Table III. Downcoming Atmospheric Radiation R and 

Effective Terrestrial Radiation E in Rel.ation to 

Vertical Temperature Distribution 



It can be seen that measurements at high atmos- 
pheric temperatures, when they are taken as represen- 
tative for OC, yield too low a downcoming radiation, 
except when the vapor content of the atmosphere is 
exceptionally low. Brunt prefers presentation by an 
exponential law and finds the radiation as proportional 
to T'-^ without indication of the vapor content. In the 
little-known formula of Robitzsch [45] for atmospheric 
radiation, R varies as aTo^. 

2. On nearly all cloudless nights during which radia- 



Inversion thickness 
(m) 


Temperature 
increase 
(deg C) 


R 
(cal cm~2 min-i) 


E 
(cal cm 2 min i) 


100 


9.4 


.360 


.099 


200 


8.8 


.356 


' .103 


300 


8.2 


.353 


.106 


400 


7.6 


.351 


.108 


500 


7.0 


.350 


.109 


1000 


0.0 


.344 


.115 


Lapse rate < 


6C km-i 
adiab. 


.334 
.333 


.125 
.126 



distribution, especially that part close to the groxmd, 
is not known. Frequently, the temperature immedi- 
ately contiguous to the ground will increase with alti- 
tude even more rapidly than assumed in the examples 
in Table III, and can thus cause an even larger positive 
deviation of the atmospheric radiation. Generally there 
will be no inversion over mountain stations, although 
so-called mountain inversions do occur. The diurnal 
variation of the temperature gradient may also explain 
the diurnal variation of the atmospheric radiation and 
its dependence on the air mass as demonstrated by 
Falckenberg [16]. 

3. Robinson [43] has carried out very careful evalua- 
tions of the measurements at Kew which included 
soundings of the free atmosphere. He found that on 
only few of the clear nights could the radiation values 
easily be fitted on a smooth curve that represented 
the relationship between radiation and the vapor con< 
tent of the atmosphere. For other nights R rose to 0.03 
cal, that is, more than 10 per cent higher. Such supple- 
mentary radiation appeared at times within an hour. 
It is impossible to seek an explanation in the variation 
of the content of CO2 or O3. It is rather more plausible 
to conceive a sudden development or advection of 
ground inversions or of very thin invisible cloud veils. 
Robinson suspects, rather, an additional radiation 



40 



RADIATION 



caused by smoke or combustion gases from the chim- 
neys of London. Quite similarly, Falckenberg [16] tried 
to explain the deviations he found for different air 
masses not by temperature gradients, but by the haze 
content which is not indicated by the water vapor. 
Volz [49] attempted to measure the emissivity of various 
substances in the laboratory. 

Robitzsch [45] pointed out another as yet unex- 
plained relationship. He established the formula 

R = aTa' (0.135p -I- e.Oeo) 

which includes not only the vapor pressure eo but also 
the air pressure p. This formula permits, in particular, 
the use in the interpolation equations of measurements 
on mountains or in the free atmosphere. Whether the 
term containing the air pressure can be attributed to 
an effect of the COi content or to a diminution of ground 
inversion with decreasing values of p (anticyclonic and 
cyclonic conditions) would have to be determined by 
future research. 

F. A. Brooks [7] and Robinson [43] developed radia- 
tion diagrams based upon observational data exclu- 
sively. The above-mentioned law for monochromatic 
radiation, according to which the radiation of an at- 
mospheric layer is equal to that of a cylindrical column 
of air with ^3 times the water-vapor content, applies 
also to the "chromatic" radiation of the natural COt 
plus H'iO atmosphere. Therefore, a radiation diagram 
for diffuse radiation can be used also for the investiga- 
tion of linear or parallel radiation arriving from a 
definite zenith distance if we multiply the vapor scale 
by 1.66. The authors cited above proceeded conversely 
and developed from the measurements of a zonal sky 
radiation a graph that was then adapted to the use of 
hemispheric radiation.^ 

Atmospheric radiation finds an important applica- 
tion in the theoretical investigation of the nocturnal 
cooling process and in the prediction of frost. It has 
been shown by various authors that the nocturnal 
cooling cannot be traced essentially to a heat emission 
of the air by radiation (see the objections raised to this 
on page 45). The decisive factor is the heat loss from 



2. (Note added July, 1950.) Robinson [44] recently published 
a detailed test of his diagram and of the Elsasser chart, for 
which he used numerous radiation measurements made at 
Kew. He found considerable differences which, to a great ex- 
tent, are caused bj' the change in the emissivitj' of a vapor 
lajrer with temperature. According to his measurements, the 
emissivity increases with increasing temperature, whereas 
according to calculations by means of the Elsasser chart, it 
decreases by an amount half that of the measured increase 
(see numerical data on page 39). The prerequisites for the 
explanation of this discrepancy are as follows: (1) new experi- 
mental investigations are needed which would furnish the 
variation of absorption by vapor la.yers of finite thickness; (2) 
the theoretical computations must be checked; the change in 
radiation with temperature is derived (a) from the displace- 
ment according to Planck's radiation law, (ft) from the change 
in the width 5 of a spectral line with\/?', and (c) from the 
change in the line intensity 5 with temperature. It appears 
that the last two influences have, to date, not been sufficiently 
considered. 



the ground by its effective radiation, and the distribu- 
tion of this heat loss through conduction into the 
ground and through convection into the air. In the 
theoretical treatment of this problem the effective ter- 
restrial radiation E = aTo^ — R was often assumed to 
be constant. However, o-To* decreases with progressive 
cooling, and R decreases with the development of a 
ground inversion, but somewhat more slowly. Groen 
[21, 22] pointed out the necessity as well as the possi- 
bility of considering the change of E with To by means 
of the radiation diagram in such a way that the equa- 
tions for the nocturnal cooling continue soluble. His 
final equation represents an important step forward 
in the theory of nocturnal cooling, especially since he 
can include in his equation the different disturbing 
influences such as initial temperature distribution, con- 
densation, and the influence of the wind on turbulent 
heat exchange. 

The Absorption CoefRcient as a Function of Pressure 

So far we assumed the absorption coefficient ky to 
be independent of pressure and temperature. However, 
that is not exactly the case. True, the variation is so 
small that the downcoming atmospheric radiation at 
the ground is not materially changed, because 88 per 
cent of it originates in the lower 500 m of the atmos- 
phere where the pressure differs little from that at 
ground level. At higher altitudes, however, the varia- 
tion is more effective. The individual absorption line in 
a band spectrum increases its half-value width with 
increasing air pressure and temperature. Yet the "total 

intensity" of the line, that is, / k^dv, is not changed. 

Only the shape of the line is altered. With increasing 
pressure it becomes wider and less intensive, with de- 
creasing pressure it becomes narrower and more in- 
tensive. This means that, as the pressure decreases, 
the absorption increases even more in the narrow center 
of the line with a large value of k,, whereas k^ becomes 
even smaller on the wings of the line [14]. As to the 
absorption by a line, it is found that, in thin layers, 
the radiation is absorbed almost completely in the core, 
whereas only in the case of thicker layers is the radia- 
tion also absorbed in the wings. With decreased pressure, 
the absorption in the core is increased and is very effec- 
tive over the first part of the optical path length. How- 
ever, subsequent absorption over the remainder of the 
path is diminished because of the small amount of 
radiant energy left to be absorbed. Since the initial 
segment can hardly be observed, the measurements 
indicate only that the mean absorption coefficient is re- 
duced [46] in proportion to \/p/po- In the absorption 
formulas k appears only in the product k ■ m . Th erefore, 
it is customary to apply the factor jj. = -s/p/po not to 
k, but to the radiating mass m or to the densities of 
water vapor and CO2. This correction is very important 
for all investigations into the radiation phenomena of 
the free atmosphere. 

The intensity S of aline, S = I k^dv, remains un- 
changed with a change of the line width S because of 



LONG-WAVE RADIATION 



41 



the simultaneous change in /,o. Hence 

SAv = A'oirS. 

If this expression is inserted into the square-root for- 
mula (page 35), we obtain 



L = \/Sm8/Av. 

The theory of line broadening by atomic collisions 
demands a simple proportionality of 5 with_ p. Conse- 
quently, the absorption L must vary as y/p. Schnaidt 
[46] emphasizes that the measurements by Falcken- 
berg show a proportionality of the absorption coefficient 
k with -x/p- This means that, when an exponential law 
is used for absorption, \/'p appears as a factor of m in 
the exponent. However, if the square-root law is used, 
the logical result is that L cc yjmy/y or L oc y/p. 
Thus, there exists a contradiction between theory and 
observation. Nowadays the tendency is to place more 
confidence in theory than in measurements. Neverthe- 
less, a repetition of the measurements would be desir- 
able. 

At the various wave lengths the transition from the 
absorption in the center to that on the flanks occurs 
with entirely differing thicknesses of vapor strata, be- 
cause of the extraordinarily great differences of the 
absorption coefficients in the water-vapor spectrum. 
This leads to a complicated interspersion of absorption 
amplification and attenuation by the air pressure at 
the same level of the atmosphere. However, Moller 
[35] has shown 'hy a rough calculation that, even on 
the assumption that h <^ p, the factor that must be 
applied to the vapor density of the atmosphere for use 
of the standard absorption equations (9), (13), and 
(15) has a value within the limits of p and \/p up to 
100 mb (16 Ian). At still greater altitudes this factor 
increases again, because at the extremely low vapor 
content of the stratosphere only the center of the very 
strongest lines absorb. Moller proposes, instead of the 
factor (U = p/po, a more complicated one, namely 

p! = 0.985 (p/po)"-* + 0.015 (p/po)-^ 

This factor has a minimum at around 100 mb and 
increases at higher levels. However, in the practical 
calculation of the cooling it is found that at these alti- 
tudes the radiation effect of water vapor becomes 
negligible owing to the greatly diminished vapor con- 
tent, and that the radiation of other absorbers pre- 
dominates. Therefore, the rigorous application of the 
correction factor m' is unnecessary, as long as there are 
no better observations available for altitudes above 
100 mb which would require more accurate calculations. 
Nevertheless, calculations to determine the effect of 
air pressure on changes of the shape of the lines have 
not been in vain; for, during the past few years, critics, 
on the basis of the necessary simplifications regarding 
this effect, questioned repeatedly the validity of cal- 
culations by means of the radiation diagrams [39]. 

Outgoing Atmospheric Radiation 

By the use of the correction factor ii for the effect of 
the air pressure, the radiation diagrams become suitable 



for investigations of the fi'ee atmosphere. For a given 
level Zi, we can calculate the downward radiation Ri 
from the atmospheric layers above it and, correspond- 
ingly, the upward radiation IJ\ from the ground and 
from the atmospheric layers below this level. In the 
radiation diagram the ground is treated as an isothermal 
gas stratum having the temperature To of the ground 
and an infinitely great content of water vapor and 
COi. The difference E^ — Ui — Ri is then the net 
radiation which penetrates the reference level in an 
upward direction. The same calculation for another 
level £2 furnishes E2. The excess radiation Eo — Ei, 
emitted bj^ the air column Az = z^ — Zi with air den- 
sity p, causes a cooling 



dT 

dt 



1 E2- El 



pCj, Zi — Zx 

which becomes for the limiting case: 



dt 



pCp dz 



(16) 



Roberts' first studies [42] of the radiation flow E 
indicated that it increases with altitude. Normally this 
increase is ^-ery uniform with altitude in a cloudless 
atmosphere having a continuous vertical distribution 
of temperature and water vapor. However, the air 
density decreases with altitude so that the cooling rate 
which amounts to about IC per day near the ground 
increases to two or three times that amount higher up 
in the troposphere. Only close to the ground and near 
the tropopause do special conditions prevail (see be- 
low). 

It seems logical to interpret the cooling of the free 
atmosphere as a radiation into space. That, however, 
is not possible, for the shielding b}^ the layers of water 
vapor above it is too great. It is, leather, a process simi- 
lar to heat conduction. Basically, radiation, just as heat 
conduction, tends to eciualize temperature dift'erences. 
Therefore, we may also try to set up for radiation an 
equation that has a form similar to that for heat con- 
duction, namely 



dT/dt = K d^T/dw\ 



(17) 



where K is a "virtual coefficient of conduction of the 
heat radiation," iv is the mass of water vapor 



= / PaCfe, 



(18) 



and p,i, the density of the water \-apor. This possibility 
was long ago developed theoretically by Falckenberg 
and Stoecker [18], and was later used as the basis of 
practical estimates bj^ Brunt [9, 10]; here we shall use it 
only for an interpretation of the cooling. Substitution 
of equation (18) into (17) gives 



dT/dt = Kyp,„-' dp^./dz, 



(7 = -oT/d:) 



which is negative, because dpw/dz < 0. In otlier words: 
The vapor masses at an equal geometrical distance 
above and below a given altitude are, to be sure, coldei' 
or warmer by the same temperature difference; but the 



42 



RADIATION 



colder vapor masses are "nearer" than the warmer ones 
in terms of radiation, because the vapor density is 
lower above that altitude than below it. Therefore, 
more heat is emitted upward than is received from 
below. Thus, the cooling in the free atmosphere exists 
by virtue of the fact that T is not proportional to w. 

This behavior of radiation, which is similar to heat 
conduction, is also clearly revealed by a break in the 
curve of vertical temperature distribution. There is an 
abrupt transition (schematically) from dT/dz = —y 
to dT/dz = at the tropopause. Hence the vapor 
particle at this point receives radiant heat from the 
mass below, but cannot emit anything to the masses at 
equal temperature above. Therefore, in the absence of 
other influences, it should become warmer. 

However, at higher altitudes the cooling does not 
depend only on a process similar to heat conduction, 
but in this case true emission occurs, that is, heat is 
radiated to space. Therefore, the amount of cooling is 
only partially due to the vertical temperature gradient 
and for the remainder to the mass of water vapor 
above and its screening effect on any heat radiation 
to space. The smaller this mass is, the greater the cool- 
ing. It was formerly assumed that the stratosphere had 
a high vapor content, or that the specific humidity re- 
mained constant with altitude.^ This assumption leads 
to vapor contents that are too large and to contra- 
dictions between the magnitude of outgoing radiation 
and the actual temperature distribution. Today it is 
known from measurements by Regener [41] and by 
Dobson and others [13] that the relative humidity 
decreases sharply just above the tropopause. A more 
recent publication by Barrett and collaborators [5] also 
confirms these results. They found a decrease in hu- 
midity from about 10 per cent at the tropopause to 
about one per cent at 30-km altitude, but with a thin 
saturated layer interposed. Therefore, these altitudes 
are already close to the upper boundary of the "water- 
vapor sphere" and the radiation of the intensive ab- 
sorption bands proceeds to space almost completely 
unscreened. Hence, the maximum of cooling lies at 
altitudes between 8 and 10 km. A calculation based on 
Elsasser's chart would shift this emitting layer to a 
somewhat lower level. 

Probably, as a third factor, the radiation by haze at 
the tropopause must be considered. The troposphere is 
always filled with haze, whereas the stratosphere, con- 
tigiious to this hazy stratum, contains very dry and 
extremely clear air (as has been confirmed by numerous 
observations from aircraft). To be sure, the nature of 
this haze is not definitely known; but, whether minute 
droplets or solid particles constitute this haze, both are 
capable of emitting thermal radiation, even in the range 
from 9 to 12 m, where the efficient "window" for out- 
going radiation exists. Thus the haze boundary at the 
tropopause causes an additional cooling which may 
reach several degrees per day. Similar effects appear 
also at haze boundaries within the troposphere [31]. 

3. In the troposphere the decrease of the specific humidity 
with altitude indicates that vapor is lost and liquefied through 
cloud formation in the ascending currents of water vapor. 



Cloud Radiation 

The great effect of clouds on atmospheric radiation 
is also based on the fact that they radiate like black 
bodies in the wave-length range of heat radiation. 
Therefore, the upper cloud surfaces emit a very great 
quantity of heat in the range from 9 to 12 ju at every 
altitude of the atmosphere where they may occur; in 
these intervals there is almost no downcoming radiation 
from above. This produces an intensive heat loss, con- 
centrated in a very thin layer. Naturally, this heat loss 
can become effective only if it is not counteracted by 
another process — as, conceivably, by an approximately 
equal absorption of radiant solar heat. However, 50 to 
70 per cent of the solar radiation is reflected (Fritz 
[19]), and of the remainder only a very small portion is 
absorbed, whereas the greater portion traverses the 
clouds as a diffuse radiative flux and reaches the earth 
as scattered sky radiation (daylight). There is almost 
no absorption of solar radiation in the clouds and thus, 
the heat emission from cloud surfaces is not compen- 
sated by the solar radiation, but acts unirti'peded as a 
heat sink in the atmosphere. Indeed, the higher such a 
cloud surface lies, the lower is the black -body radiation 
corresponding to its temperature. However, the at- 
mospheric radiation which impinges on the cloud sur- 
face from above is diminished even more, for it de- 
creases not only with temperature but also with the 
vapor content of the air situated above. Thus, the 
effective emission of the cloud increases with altitude. 

A different process takes place at the lower boun- 
dary of the cloud. This surface receives from the under- 
lying atmosphere, which is generally warmer, and from 
the ground, which is likewise warmer, a quantity of 
radiation that is greater than the black- body radiation 
emitted by the cloud in a downward direction. For this 
reason, the under surface of the cloud is heated by 
radiation from below. In this case there is also no com- 
pensation by other processes. The heating increases 
with increased altitude of the cloud, because of the 
increasing temperature difference between cloud and 
ground. 

For a very thin cloud layer whose vertical extent 
must not exceed 100 m, both processes, the heat loss 
above and the heat gain below, can be considered to- 
gether. Usually, the former is dominant, especially with 
low clouds such as stratus, and with middle clouds such 
as altostratus. If we assume that the heat budget of a 
thin cloud at an altitude of 5 Ian is distributed by tur- 
bulence and similar processes over a layer of air 1 km 
thick, we find a cooling of this mass of about 5C per 
day. A high cloud in the upper troposphere does not 
cool the air, because the radiation from below is rela- 
tively greater. In a tropical atmosphere, however, the 
conditions are quite different. The temperature differ- 
ence between ground and cloud increase continuously 
up to about 18 km because of the normal decrease of 
temperature with height in the troposphere. Even if 
the assumption of a closed cloud cover is discarded and 
a scattered cloud cover of only Mo is assumed, the heat 
balance of the cloud becomes positive at about 14 km. 
This means that even a thin cirrus cloud at this altitude 



LONG-WAVE RADIATION 



43 



receives more heat than it emits. Thus it cannot exist 
as a cloud and must evaporate. This is probably the 
reason for the phenomenon observed in the tropics, 
namely, that the highest cirrus clouds are not found 
near the stratosphere, but at an altitude of about 14 km. 
Also the diurnal variation in the cirrus clouds {i.e., dis- 
solution toward noon, re-formation toward evening), 
which has been occasionally observed in the subtrop- 
ical deserts, can probably be ascribed to the fact that 
the ground temperature is very high at noon [36]. 

A further consequence of the interaction betAveen 
absorption of radiation from below and emission upward 
is the fact that a cloud layer must develop its own in- 
ternal convection system. The absorption of heat in the 
lower portions will lead to an evaporation of the drop- 
lets, while the emission from the upper portions will lead 
to increased condensation and a descent of the heavier 
cloud. Thereby, the stratified cloud is resolved into 
individual convection cells, stratus is turned into strato- 
cumulus and altostratus into altocumulus. This process 
may take place fairly rapidly. A stratified cloud J^ km 
thick, at an altitude of about 5 km, is converted and 
"destabilized" from the isothermal state to one with 
a temperature gradient of 0.5C per 100 m in approxi- 
mately twenty minutes, whereas a similar cloud at a 
height of 2 km requires three quarters of an hour to 
complete the same change [32]. Keeping this in mind, 
it seems scarcely credible that an ordinary cloud layer 
can exist unchanged in the atmosphere for any length of 
time without being dissolved. If, in spite of the fore- 
going discussion, thin, closed, and stable altostratus 
cloud layers are observed, it becomes clear from the 
radiation calculations to what degree they must be sus- 
tained by a process which constantly re-forms them 
by new condensation. This process may be vertical 
austausch or upgliding, and its effectiveness must be 
considerable even in a cloud that appears to be stable 
and unchanging. 

Synoptic Situations and Radiation of the Free Atmos- 
phere 

It is easy to survey schematically the radiation proc- 
esses of an individual cloud. However, conditions be- 
come more complicated if it is desired to calculate 
approximately the effect of the clouds under different 
weather conditions or in different climatic regimes. 
Nevertheless, such calculations are necessary, since they 
offer the first possibilities for surveys. An attempt in 
this direction [36] is reproduced in Fig. 4. In this figure 
the average cloud conditions of a low-pressure area in 
middle latitudes are assumed, that is, 10 per cent of the 
area is clear, 20 per cent has clouds resting on the 
ground, 50 per cent has clouds with the lower level 
between and 2 km, and 20 per cent has clouds with 
the lower level between 2 and 8 km. Correspondingly, 
in 40 per cent of the total low-pressure area, the upper 
cloud boundary is assumed to lie between and 3 km, 
in 20 per cent between 3 and 8 km, and in 30 per cent 
between 8 and 10 km. In the average cooling curve 
shown in Fig. 4, the heat loss of the most important 
cloud levels at 2 and 9 km is distinctly noticeable, the 



lower by a cooling of almost 2C per day, the upper by 
more than 5C per day, for at this level the heat loss by 
the radiating upper cloud surface becomes more effec- 
tive because of the reduced density of the air. The hori- 
zontal distribution in the low-pressure system cannot 
be distinguished, because the various factors are aver- 
aged over the entire area. However, the cooling rate 
must be about three times as great in the advance 
portion of the cyclone where the upgliding cloud screen 
lies as a closed, though loose and diffuse, cover at 8 km 
altitude. It is obvious that such a cooling of 15C per 
day will noticeably influence the weather development 
and the cloud dynamics. Further investigations of this 
kind should yield valuable insight into the thermo- 
dynamics of weather. 




6 5 4 3 2 

COOLING (°C PER DAY) 
Fig. 4. — Cooling of the atmosphere by water-vapor radia- 
tion in degrees per day. The dashed line applies to a cloudless 
atmosphere and the solid line to an average distribution of 
clouds in a low-pressure area. 

In 1935 the author tried to give a balance of all heat- 
ing and cooling processes in the free atmosphere and 
their vertical distribution [29], in which not only the 
outgoing radiation but also the incoming solar radiation 
and the liberation of the latent heat of condensation 
were considered. The calculations for long-wave radia- 
tion will be revised here. 

A normal temperature and humidity distribution for 
middle latitudes was assumed as a basis for the calcu- 
lations. The cooling of the cloudless atmosphere, as now 
computed, differs from the earlier calculation. At that 
time, the cooling of the entire troposphere was found 
to be constant at IC per day. In the new calculation 
(Fig. 5, curve ^4) it increases with altitude to 2;^4C 
per day (at 9 km). The cause of this difference lies in 



44 



RADIATION 



part in the use of the improved radiation diagram, but 
jprincipally in the realization that the water-vapor con- 
tent of the stratosphere is much lower than was formerly 
assumed. For this reason — as mentioned above — the 
main emission level is shifted down to the altitude of the 
tropopause. The importance of reliable measurements 
of the water-vapor content of the stratosphere for these 
investigations cannot be over-emphasized, for a higher 
water-vapor content sharply reduces the emission at the 
Jievel of the tropopause. So far only two or three meas- 
urements of the frost point have been published. They 
show an unchanged decrease above the tropopause 
[131 sometimes interrupted by thin saturated layers 
[5]; however, we do not know whether, for example, the 
"Avater-vapor content over low-pressure areas is higher 
than shown by these measurements. There is consider- 
able evidence for this supposition, for otherwise how 
should the mother-of-pearl clouds observed in Norway 
•develop in the rear portion of cyclones at an altitude of 
■.28 km, if the relative humidity remains at 1 per cent 
.and less from an altitude of 14 km upward? If the 
ihumidity is greater, the radiation processes of the 
itropopause are reduced considerably. 

It is also very difficult to make any reasonable state- 
ments concerning the distribution with altitude of the 
upper cloud boundaries. It is here assumed that this 
boundary lies between and 2 km in 15 per cent of all 
cases, between 2 and 5 km in 45 per cent, between 5 and 
8 Ion in 30 per cent, and between 8 and 10 km in 10 per 
•cent of all cases. For the lower cloud boundaries, 80 per 
•cent are assumed to lie between and 3 km, and 20 
per "cent between 3 and 10 km. Consideration of these 
values gives a cooling of the free atmosphere on com- 
pletely overcast days as shown in Fig. 5, curve B, that 
is, there is a "radiation screen" in the lowest layers, 
but above 2 km there is an increase of heat loss of about 
€.8 to 1 degree per day as compared to a cloudless at- 
mosphere. On the whole, however, the difference be- 
tween the cloudy and the clear atmosphere is small. 
The calculation made in 1935 (under the assumption 
of a somewhat different cloud distribution) gave the 
greatest cooling at an altitude of 4 km. This might well 
be taken as an indication of the importance for these 
investigations of more accurate data respecting the 
distribution of the clouds in the atmosphere not onljr 
on the average, but also for specific weather situations. 

An example from an altogether different climatic 
regime also shows this very clearly. An entirely differ- 
ent temperature and cloud distribution must be as- 
sumed for a winter month at the earth's cold pole 
situated approximately in northeastern Siberia. On 
cloudless days (50 per cent of all days) the temperature 
at ground level is assumed to be — 50C, rising to — 25C 
at 1.5 Icm, and decreasing to — 60C at 8-km altitude. 
In the presence of a cloud cover, the temperature be- 
tween and 2 km is taken to be constant at — 30C. 
The clouds, which are seldom very massive (there are 
only two days of precipitation per month) , are assumed 
to be restricted to the layer between 0.5 and 2 km. 
On clear, as well as on cloudy days, an extremely strong 
cooling layer results between 1 and 2 km, with an 



average of 5C per day (Fig. 5, curve D). Aloft the 
cooling is comparatively slight. Thus the vertical ar- 
rangement of the heat balance in this continental winter 
climate deviates considerably from that of our middle 
latitudes under maritime influence. 

As a third example, a tropical atmosphere is repre- 
sented (Fig. 5, curve C). There is little difference up to 
7 km as compared to the temperate latitudes. The 
maximum of the outgoing radiation lies at an altitude 
of 13 I'on and is not affected by processes resembling 
heat conduction as in the temperate tropopause at 
10 km. This appears to be an approach to a solution of 




-4 -3 -2 -I +1 

TEMPERATURE CHANGE ( °C PER DAY) 

Fig. 5. — Temperature change of the atmosphere by water- 
vapor radiation in degrees per day. 

(A) Normal atmosphere in middle latitude, cloudless. 

(B) The same with an average distribution of clouds. 

(C) Tropical atmosphere, cloudless. 

(D) Temperature and cloud disti-ibution at the cold pole. 

the old problem concerning the origin of the tropo- 
pause. In middle latitudes we find the maximum of 
heat loss in the region of the tropopause. There, it may 
be a fair assumption to consider the water-vapor radia- 
tion as the cause of the tropopause. In the tropics, 
the layer of strongest cooling lies about 4-5 km below 
the tropopause. Thus, it is most probable that the 
tropopause is produced in a different manner in the 
tropics than in temperate latitudes. Whether steady- 
state dynamic phenomena play a role here, or whether 
the C02-radiation becomes important, remains as yet 
unexplained. Explanations which distinguish between 
the tropopause in temperate and in tropical regions have 
also been developed by Goody [20]. Finally, further 
indication is given by the abi-upt discontinuity in the 
altitude of the tropopause at lat 30°, which was sus- 



LONG-WAVE RADIATION 



45 



pected as early as 1935 [30] and which was recently 
demonstrated by Hess [23]. 

Radiation cannot be responsible for day-to-day 
changes in the tropopause of the temperate latitudes, 
since its effect is much too slow, as shown by Junge 
[26]; in this case dynamic processes are certainly im- 
portant. On the average, however, radiation of water 
vapor is as responsible for the low temperature at the 
tropopause, as is the decrease of solar radiation from 
the equator to the pole for the meridional temperature 
distribution of the troposphere, although in the latter 
case, day-to-day variations are likewise considerable. 

Numerical and Analytical Radiation Calculations 

All calculations of radiation processes mentioned so 
far are based on the method of the radiation diagrams. 
There is no doubt that these are somewhat cumber- 
some. The determination of the heating and cooling 
processes via the radiation fluxes and their differentia- 
tion with respect to altitude seems especially laborious. 
Bruinenberg [8] has made a valuable contribution here 
toward attaining the objective directly. He puts the 
differentiation with respect to altitude, which can also 
be replaced by differentiation with respect to tempera- 
ture, under the integral of the radiative flux in equation 
(13) or (15). Thus, after calculations of a scope analo- 
gous to those required for the construction of a radia- 
tion diagram, he arrives at expressions which are suit- 
able for numerical integration or summation. However, 
these equations are less suitable for a graphical treat- 
ment. Therefore, Bruinenberg has calculated tables 
which permit very simply the determination and addi- 
tion of the cooling or heating effects exerted on a given 
element by all atmospheric layers above and below it. 

The principal advantage of the individual calcula- 
tion is the fact that the cooling for points closely spaced 
along the vertical can be determined independently and 
with great accuracy. This leads to a result which, though 
not unexpected, has thus far been underestimated in 
its implications. Every break in the vertical tempera- 
ture distribution is manifested as a .sharp peak in the 
distribution of the cooling rate. Thus cooling peaks up 
to 3C per day project from the average cooling level 
of IC per day in the lower troposphere at every break 
of the characteristic temperature curve directed toward 
higher temperatures, and heating peaks up to -f IC 
or -f2C per day where the characteristic curve breaks 
toward lower temperatures. Heating of +5G per day 
occurs below an inversion, whereas there is a cooling 
of 15C per day at its upper boundary. However all this 
holds true only in very thin layers. (Bruinenberg's 
method is so far applicable only to calculations in the 
lower and middle troposphere; for the tropopause, see 
p. 42.) At these points the radiation simply acts as a 
temperature equalizer in a manner similar to heat con- 
duction. Every break in the characteristic temperature 
curve is equalized at an accelerated rate. From the fore- 
going discussion it follows again that if inversions or 
more or less sharp discontinuities in the temperature 
gradient persist for days, the ordinary radiation proc- 
esses of the water vapor cannot be the cause. Thus the 



question whether long-wave radiation can produce in- 
versions is decided partially in favor of the negative 
[4]. For the maintenance of existing inversions, some 
processes must be constantly active that recreate the 
inversion continuously against the equalizing effects of 
the radiation. Such processes are partly the additional 
radiation from the haze layers below the inversion which 
overcompensate the heating (see p. 42) and partly the 
dynamic processes of shrinking and subsidence. The 
intensity of these dynamic processes can then be esti- 
mated from the calculations of radiation. 

An especially significant level is the earth's surface. 
For radiation effects, the ground may be conceived as 
replaced by an infinitely extended isothermal layer of 
water vapor or CO2. In such a case the corresponding 
characteristic temperature curve extended into the 
ground has a break at the ground surface. If there is a 
temperature decrease with altitude above the ground, 
there must be strong cooling directly at the ground 
surface, whereas there is strong heating at the base of a 
ground inversion. Such radiative processes will scarcely 
become operative, since all observations disprove them. 
However, in every case, they will tend toward an iso- 
thermal state near the ground as an equilibrium con- 
dition. Even if this equilibrium is not reached, its quan- 
titative consideration will possibly lead to a revision of 
the assumptions concerning the magnitude of the aus- 
tausch near the ground as far as has been disclosed by 
measurements of the temperature gradient." 

Although the graphical and numerical calculation 
methods are carefully worked out, an analytical equa- 
tion can be very advantageous at times because it per- 
mits combination of the radiation process with others 
that can be approached theoretically. Such a possi- 
bility is offered by the quasi-conduction of radiation 
introduced by Brunt [9]. However, this method will not 
include the processes at the ground surface which were 
discussed above. The complicated construction of a 
radiation diagram makes it apparent that a complete 
description by a single convenient equation is impos- 
sible. Simplifications must be made. One such simplifi- 
cation consists of running the temperature lines hori- 
zontally in the Moller diagram (in the water-vapor 
section). This means that we do not change the distribu- 
tion of the absorption coefficients over the wave lengths, 
but that we do assume that the energy curve has the 
same shape for all temperatures, instead of assuming 
Planck's formula for black-body radiation. This would 
imply, for example, that, if we take the shape of the 
energy distribution at 273K, the radiation for a differ- 
ent temperature would be given by multiplying this 
curve by the factor 7'V273'' which is not a function of 
the wave length. In the Elsasser chart this assumption 
would mean that the tt'-lines would be rectilinear and 
convergent to the point where T =0K. If, in addition, 
we approximate the abscissa scale X of the Moller chart 
with any convenient function, new problems can be 
solved. 



4. (Note added July, 1950.) In hi.s newest publication, Rob- 
binson [44] also comes to the conclusion that radiation processes 
are very important near the earth's surface. 



46 



RADIATION 



An initial attempt of this type was made by approxi- 
mating the function X by the sum of two exponential 
functions. This would mean that the absorption spec- 
trum of the water vapor is not gray but "bichromatic." 
The investigation of the radiation equilibrium of the 
atmosphere was carried out by Emden [15] for gray 
radiation and led to an isothermal stratosphere of 
— 68C. The calculation of the same problem for bi- 
chromatic absorption of water vapor does not lead to 
an isothermal stratosphere but yields a steady decrease 
in temperature with altitude down to — 144C at the 
boundary of the atmosphere [31]! If it still were at all 
necessary to deal the death blow to the untenable 
theory of the radiation equilibrium of the water vapor 
in the stratosphere, this calculation would do so. 

Another approximation of X is fundamentally more 
accurate. If we set X = a ln(w + b), where a and b 
are numerical values, we obtain an approximation 
that is especially good for small values of w and small 
amounts of CO2. Then dX = adw/(w -f b), and from 
this simple formula the radiation equilibrium can be 
developed as a kind of integral equation and can be 
brought closer to numerical solution. This method 
appears important especially for the temperature 
distribution in immediate proximity to the ground be- 
cause, under conditions of both midday adiabatic strat- 
ification and nocturnal ground inversion, this tempera- 
ture distribution is a function not only of the austausch 
but also of radiation. Results of these calculations are 
not yet available. 

Radiation in the Stratosphere 

Investigation of radiation phenomena in the strato- 
sphere is more difficult than in the troposphere for sev- 
eral reasons. First of all, the absorbing media are under 
very low pressure, and therefore a check must be made 
in every case to ascertain to what extent the absorption 
coefficients, as measured in the laboratory, may be 
used. In the second place, the concentration of the 
various gases is not known exactly. Finally, the radia- 
tion cannot be considered any longer as an individual 
process out of the context of the general physical phe- 
nomena. In the troposphere also, radiation participates 
everywhere, to be sure, in the general Aveather pattern, 
and in the presentation above, emphasis has been on 
showing that radiation participates decisively in all 
meteorological processes. However, the substances 
themselves are not changed in their molecular struc- 
ture by absorption or emission. If, for instance, water 
vapor is brought to condensation and fog forms as 
a result of strong radiational cooling, it changes only 
its aggregate state, not its chemical structure. In the 
stratosphere, however, ozone offers an example of more 
drastic changes. It is only by the absorption of the solar 
radiation in the ultraviolet bands that the formation of 
O3 from O2 becomes possible, and it is under the in- 
fluence of longer waves in the ultraviolet that the ozone 
again dissociates. It is indeed true that it is not the 
long-wave heat radiation but the short-wave solar radi- 
ation that controls the formation and dissociation of the 
absorbing medium. In addition, however, both proc- 



esses participate in the heat balance with their thermal 
implications. Therefore, the radiation processes in the 
stratosphere cannot be separated from the multitude of 
physical atomic processes at those altitudes. If, in spite 
of this, such an attempt is made, it will necessarily be 
in full consciousness of the unreliability involved. 

Above 10-km altitude the importance of water vapor 
as a decisive absorbing medium decreases more and 
more, and CO2 and O3 become significant. The water- 
vapor content of the air in the stratosphere is extremely 
small according to measurements by Dobson [13], Bar- 
rett [5], and others. For several kilometers above the 
tropopause the frost point falls steadily at the rate of 
its decrease with altitude in the troposphere, so that 
the relative humidity at 2 km above the tropopause 
has decreased to below 1 per cent. However, if we 
accept this low humidity as a generally valid fact, the 
radiation effect of the water vapor in the stratosphere 
no longer exerts any notable effect, since its total 
content drops to 10~* g cm~^. Dobson, however, thinks 
that its effect is to be considered equivalent to that of 
CO2, but gives no numerical values for the amount of 
absorbed radiation. 

Carbon dioxide has a very intensive absorption band 
around 15 n. An extremely weak band around 10 jn 
absorbs only one per cent for layer thicknesses that 
equal the content of the whole atmosphere. An addi- 
tional band at 4 ^i lies at the boundary of the spectrum. 
The absorption curve in the 15-/i band is known. The 
dependence on pressure is usually estimated by the 
effect on the 4-ai band which is known from measure- 
ments by Wimmer [51]. From this Moller has derived 
a redu ction factor n = (p/po)"-'*, whereas Elsasser uses 
the -x/p/po law in the same manner as for the water 
vapor, and Goody a proportionality to p. A calculation 
of the processes is possible by means of the Moller dia- 
gram. Moller calculated the C02-radiation emitted by 
an isothermal stratosphere and found a maximum effect 
at an altitude of 26 km with a cooling of 1.5C to 2C 
per day. Since his assumption of a COa-content of 0.03 
per cent is somewhat too high, the maximum lies prob- 
ably a little lower. 

In this calculation it was assumed that the ozone has 
no effect. But, as mentioned already, ozone has a very 
intensive absorption band around 14 ju which is situated 
at the same point as that of CO2 and shows a curve 
with respect to wave length which is similar to that of 
CO2. The line structure of ozone which probably differs 
from that of CO2, is unknown, however, and probably 
does not enter into the calculations. Since half of the 
ozone lies at altitudes above 20 km, the radiation of the 
CO2 is extensively shielded by its absorption, and the 
outgoing radiation in this range of wave lengths takes 
place only at higher altitudes and then as an emission of 
the ozone. Thus, these processes interact strongly with 
each other, and for this reason scarcely any attempts 
have been made to investigate them in greater de- 
tail [33]. 

Furthermore, the experimental bases for the ozone 
spectrum are not yet sufficient. In addition to the 
14-m band, there is another band around 9.6 ju, which 



LONG -WAVE RADIATION 



47 



lies exactly in the "window" of the water vapor and 
which therefore can contribute to the effectiveness of 
the outgoing radiation emitted by the earth's surface 
despite the weak absorption and the small amount of 
ozone. Adel [2] measured the intensity of the solar 
spectrum at this wave length in an excellent experi- 
mental investigation and was able to detect the absorp- 
tion in this band. Its maximum is about 50 to 70 per 
cent. The old laboratory measurements by Hettner 
and collaborators [24] were made on large amounts of 
ozone under high pressure. From their absorption co- 
efficients and the normal amount of ozone in the atmos- 
phere the maximum absorption found at 9.6 n is only 
14 per cent. This contradiction was explained by Strong 
[47], who made measurements with ozone under low 
total pressures. He was able to show that the supple- 
mentary atmospheric pressure greatly broadens the 
absorption lines of ozone, whereas an increased partial 
pressure causes only a minor broadening of these lines. 
It is for this reason that the absorptions measured in 
pure ozone without admixture of air are much too small 
in spite of large quantities of ozone. The application of 
the absorption values as measured by Strong leads to 
a maximum absorption at 9.6 /j, equal to that found in 



gradient, namely from 6C per km in the troposphere 
to isothermal conditions in the stratosphere. By means 
of separate calculations of the individual bands of the 
three absorbers, water vapor, carbon dioxide, and ozone, 
he investigated the radiation balances and their de- 
pendence on barometric pressure and temperature at 
the tropopause. He found that in middle and high 
latitudes an equilibrium exists between the heating 
effect of carbon dioxide and the cooling effect of water 
vapor; in the tropics, however, water vapor, because of 
its extremely small concentration, no longer has any 
effect. There, an equilibrium exists between the effects 
of carbon dioxide and ozone. At the great heights and 
the low temperatures of the tropical tropopause, how- 
ever, carbon dioxide has a cooling effect, ozone a very 
faint heating effect. This led Goody to the remarkable 
concept that radiative equilibrium always depends on 
the contrast between two different absorbers, and that 
in the tropics the participating media are different from 
those in middle latitudes. The quantitative bases of 
these computations appear to be still inadequate. For 
this reason, verification would be most desirable. Also, 
it appears to this writer that the selection of the tropo- 
pause for these calculations is somehow not quite suit- 



Table IV. Radiational Heating of the Stratosphere {According to Oder [38]) 






h (km) 


15 


20 


25 


30 


35 


38 


41 


44 


47 


aT/at (deg C per day) 

3T/9t (deg C per hour) 


0.1 


-0.6 


-0.5 


3.1 


(-44) 
-1.8 


(-120) 
-5.0 


(-172) 
-7.2 


-98 
-4.1 


3.3 







the solar spectrum. Though these processes are ex- 
plained for the 9.6-/X band, this is not true for the 14-/^ 
band for which similar measurements are completely 
lacking. In this case we must depend on analogous con- 
clusions. 

Through numerous investigations we are well in- 
formed concerning the amount of ozone in the atmos- 
phere and its vertical distribution. Only recently were 
the optical determinations of this vertical distribution 
excellently confirmed by direct measurements. Pre- 
vious calculations of the radiation phenomena in the 
ozone (Gowan, Penndorf) are based on the uncorrected 
laboratory measurements of the absorption by Hettner. 
The results are therefore incorrect. Recently, a new 
calculation was made by Oder [38]. He uses values for 
the absorption coefficient which in each case give only 
an average for the whole band. This incorrectly distorts 
the absorption function, and his results are therefore 
apparently inaccurate. However, the numerical values, 
which are presented in Table IV, are noteworthy. 
At an altitude of about 40 km the emission of radiant 
heat produces a cooling of about 8C per hour. It will 
not be very easy to explain what processes compensate 
for this large cooling, but they must be compensated 
somehow if the assumption that the temperature dis- 
tribution remains stationary is correct. Goody [20] 
made the most important contribution to the theory 
of radiation of the tropopause. He assumed that in this 
region a discontinuity exists in the vertical temperature 



able because of the peculiarities of radiative processes 
at points of discontinuity in the temperature gradient. 
However, it is difficult to suggest altitudes that would 
be more suitable for such computations.* 

Suggestions for Future Research 

Though the foregoing exposition touched only briefly 
on the experimental foundations, it has nevertheless 
been shown that the most important lines along which 
research must now proceed are of an experimental or 
observational nature. The following appear to the au- 
thor to be of particular importance: 

1. Absorption or emission of water-vapor layers of 
limited thickness must be checked by laboratory and 
free-air experiments. The available measurements seem 
insufficient to explain the variation with temperature 
that results from the variation of the observed atmos- 
pheric radiation. Such measurements are a very impor- 
tant basis for radiation diagrams and fo r all conclusions 
drawn from them regarding the free atmosphere. 

2. Long-wave radiation, particularly in the free at- 
mosphere, must be measured. Since there are filter 
substances available which are not only very good in 
the long-wave range but which are uniform for all wave 
lengths [25], there should be no basic difliculty in con- 



5. (Note added July, 1950.) A recent investigation by Plass 
and Strong [40] may clarify this problem. However, only an 
abstract of this work has been published thus far , 



48 



RADIATION 



structing instruments to be mounted in aircraft. This 
would shift investigations into entirely new channels. 

3. Adequate data concerning the content of water 
vapor and carbon dioxide of the upper troposphere and 
the lower stratosphere are needed for investigation of 
tropospheric radiation by means of the familiar graphical 
methods. Spot checks are inadequate. Measurements 
are needed in such numbers that radiation changes 
with the weather situation become clear. The influ- 
ences of the geographical latitude and of continents 
and oceans on the content of water vapor and carbon 
dioxide must also be determined. The same holds true 
for the determination of the upper cloud boundary 
for various weather patterns and various types of cli- 
mate. Radiosonde observations are not sufficient for 
this purpose; direct observations from aircraft are 
needed. We must consider such observations as the 
principal demand which radiation research makes on 
the field of observational aerology. 

4. The influence of pressure on the absorption by 
CO2 and O3 in the 15-fj. band must still be investigated 
in the laboratory for application to the study of the 
radiation processes in the region of the tropopause. 
Only then can we approach an explanation of the radi- 
ation processes at these altitudes with any hope of suc- 
cess. 

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1. Adel, a., "Absorption Line Width in the Rotation Spec- 

trum of Atmospheric Water Vapor." Phys. Rev., 71: 
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2. and Lampland, C. O., "Atmospheric Absorption of 

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3. Angstrom, A., "Messungen der nachtliohen Ausstrahlung 

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4. AsHBURN, E. v., "The Vertical Transfer of Radiation 

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5. Barrett, E. W., Herndon, L. R., Jr., and Carter, H. J., 

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6. BoLZ, H. M., und Falckenberg, G., "Neubestimmung der 

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9. Brunt, D., "The Transfer of Heat by Radiation and Tur- 

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"Meteorology of the Lower Stratosphere." (Bakerian 
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58:415-417 (1941). 

18. Falckenberg, G., und Stoecker, E,, "Bodeninversion und 

atmospharische Energieleitung durch Strahlung." 
Beitr. Phys. frei. Atmos., 13: 246-269 (1927.) 

19. Fritz, S., "Measurements of the Albedo of Clouds." Bull. 

Amer. meteor. Soc, 31 : 25-27 (1950). 

20. Goody, R. M., "The Thermal Equilibrium at the Tropo- 

pause and the Temperature of the Lower Stratosphere." 
Proc roy. Soc, (A) 197: 487-505 (1949). 

21. Groen, P., "Note on the Theory of Nocturnal Radiational 

Cooling of the Earth's Surface." J. Meteor., 4: 63-66 
(1947). 

22. "On Radiational Cooling of the Earth's Surface 

during the Night, Especially with Regard to the Pre- 
diction of Ground Frosts." Meded. ned. meteor. Inst. 
(B) Deel I, Nr. 9 (1947). 

23. Hess, S. L., "Some New Mean Meridional Cross Sections 

through the Atmosphere." /. Meteor. 5: 293-300 (1948). 

24. Hettner, G., Pohlmann, R. und Schumacher, H. J., 

"Die Struktur des Ozon-molekiils und seine Banden im 
Ultrarot." Z. Phys., 91 : 372-385 (19.34). 

25. Jogs, G., "Optische Eigenschaften der festen Korper." 

Naturforschung und Medizin in Deutschland, 1939-1946 
(FIAT Rev.). Wiesbaden, Dieterich Verlag, 1948. (See 
Vol. 9, Pt. 2, pp. 164-184) 

26. Junge, C, "Zur Strahlungswirkung des Wasserdampfes 

in der Stratosphare." Meteor. Z., 54: 161-164 (1937). 

27. LiNKE, F., Meteorologisches Taschenbuch, 4. Aufl. Leipzig, 

Akad. Verlagsges., 1939. (See p. 262) 

28. und MoLLER, F., "Langwellige Strahlungsstrome in 

der Atmosphare und die Strahlungsbilanz," Handbuch 
der Geophysik, Bd. 8, Kap. 11. Berlin, Gebr. Borntrager, 
1943. (See pp. 668-721) 

29. MoLLER, F., "Die Warmequellen in der freien Atmosphare." 

Meteor. Z., 52: 408-412 (19.35). 

30. "Hohenwindmessungen und horizontales Temperatur- 

feld." Beitr. Phys. frei. Atmos. 22: 299-307 (1935). 

31. "Die Warmestrahlung des Wasserdampfes in der 

Atmosphare." Beitr. Geophys., 58: 11-67 (1941). 

32. "Labilisierung von Schichtwolken durch Strahlung." 

Meteor. Z., 60; 212-213 (1943). 

33. "Zur Erklarung der Stratospharentemperatur." Na- 

turwissenschaften, 31:148 (1943). 

34. "Das Strahlungsdiagramm." Wiss. Abh. D. R. Reich. 

Wetterd. (1943). 

35. "Grundlagen eines Diagramms zur Berechnung lang- 

welliger Strahlungsstrome." Meteor. Z., 61 : 37-45 (1944). 

36. "Wirkungen der langwelligen Strahlung in der At- 
mosphare." Meteor. Z., 61: 264-270 (1944). 

37. MiJGGB, R., und Moller, F., "Zur Berechnung von Strah- 

lungsstromen und Temperaturanderungen in Atmos- 
pharen von beliebigem Aufbau." Z. Geophys. 8: 53-64 
(1932). 



LONG-WAVE RADIATION 



49 



38. Oder, F. C. E., "The Magnitude of Radiative Heating in 

the Lower Stratosphere." /. Meteor., 5: 65-67 (1948). 

39. Pedersen, F., "On the Temperature-Pressure Effect on 

Absorption of Long-Wave Radiation by Water Vapour." 
Meteor. Ann. Oslo, VoL 1, No. 6, pp. 115-136 (1942). 

40. Plass, G. N., and Strong, J., "Radiation Equilibrium in 

the Stratospliere." Phys. Rev., (2) 78: 334 (1950). 

41. Regener, E., "Aufbau und Zusammensetzung der Strato- 

sphare." Schr. dtsch. Akad. Luft.,SS. 7-41 (1939). 

42. Roberts, 0. F. T., "On Radiative Diffusion in the Atmos- 

phere." Proc. roy. Soc. Edinb., 50: 225-242 (1929-30). 

43. Robinson, G. D., "Notes on the Measurement and Esti- 

mation of Atmospheric Radiation." Quart. J. R. meteor. 
Soc, 73: 127-150 (1947). 

44. "Notes on the Measurement and Estimation of At- 
mospheric Radiation — 2." Quart. J. R. meteor. Soc, 76: 
37-51 (1950). 

45. RoBiTzscH, M., "Strahlungsstudien." Arb. preuss. aero. 
06s., 15: 194-213 (1926). 



46. ScHNAiDT, F., Uber die Absorption von Wasserdampf und 

Kohlensaure mit besonderer Berilcksichtigung der 
Druck- und Temperaturabhangigkeit." Beitr. Geophys., 
54: 203-234 (1939). 

47. Strong, J., "On a New Method of Measuring the Mean 

Height of the Ozone in the Atmosphere." .7. Franklin 
Inst., 231: 121-155 (1941). 

48. "Study of Atmospheric Absorption and Emission in 

the Infrared Spectrum." J. Franklin Inst., 232: 1-22 
(1941). 

49. VoLZ, F., Untersuchungen iiber den Einfluss der Triibung 

auf die langwellige Strahlung in der Atmosphare. Diplom- 
Arbeit, Meteor. Inst. Frankfurt/M., 1950 (unpublished). 

50. Wexler, H., "Observations of Nocturnal Radiation at 

Fairbanks, Alaska, and Fargo, N. Dak.," Mon. Wea. 
Rev. Wash., Supp. No. 46 (1941). 

51. WiMMER, M., "tjber die Beeinflussung der ultraroten 

Kohlensaureabsorptionsbande bei 4.27 m duroh fremde 
Gase und ihre Anwendung zur Gasanalyse." Ann. 
Physik., 81: 1091-1112 (1926). 



ACTINOMETRIC MEASUREMENTS 

By ANDERS ANGSTROM 
Meteorological and Hydrological Institute of Sweden 



ACCURACY OF ACTINOMETRIC 

MEASUREMENTS 

In actinometry, as in every other field of science 
founded upon some kind of direct measurement, the 
instrumental accuracy and the method of observation 
must be closely related to the character of the scien- 
tific problem under consideration. 

Determination of the Solar Constant. Some scientists 
maintain that this so-called "constant" is subject to 
short periodic variations amounting to approximately 
0.2 per cent on the average, with a maximum amplitude 
of about 1-2 per cent. It is evident that in order to 
investigate these variations our measuring devices must 
be sufhciently accurate to measure amounts of radia- 
tion below the smallest amplitude of the variations 
which we intend to determine, in other words, the 
instrument must measure accurately to at least ±0.2 
per cent. 

Heat Exchange at the Earth's Surface. Considerably 
less accuracj' is required in manj^ other problems closely 
connected with actinometry. Suppose, for instance, 
that we wish to investigate the heat exchange at the 
earth's surface through radiation, convection, conduc- 
tion, evaporation, etc. Here, the radiation enters into 
an equation in which the other factors involved can 
hardly be determined to an accuracy greater than 
5-10 per cent. Even if we could measure them more 
accurately, it would be of little benefit, since the values 
have no general applicability. Convection, conduction, 
reflection from the earth's surface, and evaporation are 
all highly variable from place to place. Local measure- 
ments are seldom representative for more than very 
limited areas. An accuracy of ±3 per cent seems in 
general quite sufficient for such purposes as actino- 
metric measurements aiming at an evaluation of the 
heat balance at the earth's surface, ablation studies on 
glaciers and snow covers, and studies of similar geo- 
physical problems. 

Analysis of the Atmosphere. Actinometric measure- 
ments are, however, also an important means for the 
analysis of the content of the various atmospheric con- 
stituents. Through rather simple measurements of the 
total direct solar radiation and of the same radiation 
within a few selected regions of the spectrum, an evalua- 
tion can be made of the total water content in the path 
of the solar beam as well as of the turbidity {i.e., the 
content of solid or liquid particles which scatter light in 
the atmosphere). The principles on which such deter- 
minations of the turbidity and water content are 
founded will be briefly summarized in the following 
paragraphs. 

If the solar "constant" is regarded as a true constant 
and its relatively small variations are neglected, the 



variations of the incoming direct solar radiation Qm 
at a given solar elevation (air mass = m) may be re- 
garded as due to four principal causes: 

1. The variable distance between sun and earth. 

2. Molecular scattering. 

3. Scattering and absorption by liquid and solid 
particles in the atmosphere. 

4. Selective absorption by the gases of the atmos- 
phere. 

The variations resulting from the first cause are well 
kno\vn and easily computed. The scattering by the 
molecules may be computed from the theory of Ray- 
leigh; the scattering coefficient thus determined is a 
continuous function of the wave length, being inversely 
proportional to its fourth power. 

Scattering by the solid and liquid particles in the 
atmosphere may, as a first approximation, also be 
regarded as a continuous function of the wave length. 
Strictly speaking, if the physical nature of the particles 
is kno\vn in detail, the scattering coefficient may be 
computed as a function of the wave length, according 
to the classical theory of Mie. However, since we seldom 
or never have a complete knowledge concerning the 
variable nature of the scattering particles in the at- 
mosphere, it seems allowable to introduce a simplifica- 
tion based on empirical results. From Abbot's extensive 
observations in various parts of the world the present 
author found that the scattering coefficient S due to 
liquid and solid particles in the atmosphere may, in 
general, be expressed by 



S = fi/\\ 



(1) 



where ^ has a value proportional to the number of 
particles, and a no longer has a value of 4.0 as in the 
case of the molecules but varies between 0.5 and 2.0, 
according to the size of the particles. The smaller the 
particles, the larger is the value of a. In general, an 
acceptable average value for a, that holds for ordinary 
conditions, seems to be 1.3. When the atmosphere has 
been polluted with larger particles, as after violent 
volcanic eruptions or through dust storms over deserts, 
the value of a is sometimes as low as 0.5 or even less. 
The particles influencing the visibility in the atmosphere 
near the ground are also, evidently larger than the 
average particle causing the scattering of the solar 
beam. For these lower layers Schmolinsky [10] found 
an average value of about 0.9 for a. 

These considerations hold approximately for the 
visible part of the solar spectrum, that is, for wave 
lengths in the range from 0.4 to 0.8 ix. They are, how- 
ever, not applicable to the ultraviolet and the far 
infrared. Finally, the incoming solar beam is weakened 
also by the selective absorption by the various atmos- 



SO 



ACTINOMETRIC MEASUREMENTS 



51 



]jheric gases, especially bj' water vapor and carbon 
dioxide. This absorption is not a simple function of the 
wave length, but is concentrated in certain spectral 
regions. The conditions are, however, simplified by the 
fact that the selective absorption by the variable gases 
is almost entirely confined to the far red and the infra- 
red, where the principal water-vapor and carbon dioxide 
bands occiu-. Only a small part, about 1-2 per cent of 



e 
o 




3 4 

AIR MASS, m 

Fig. 1. — Atmospheric turbidity ;8 according to Angstrom- 
Hoelper. Ordinate: total radiation measured (Q,„), with addition 
of water vapor absorption (F). Abscissa: air mass (unit vertical 
air mass at sea level and 760 mm). Actinometrio scale: Smith- 
sonian. 

the total energy is subject to a variable absorption 
within the visible and the ultraviolet. 

Consequently, the total incoming solar radiation 
Qm, as measured for instance with a pyrheliometer, may 
be expressed as 



Q,n = f /oxg" exp (-/3m/X°) d\ - F. 

•10 



(2) 



In this ecjuation we may assume Q,n to be known from 
measurements; /ox, the radiation outside the atmos- 
phere at the wave length X, is known from the elaborate 
investigations by the Smithsonian Institution (Abbot 



and collaborators);' q, the transmitted fraction of the 
incident energy for unit air mass (if only molecular 
scattering is considered), is computed from the theory 
of Rayleigh,^ the air mass m is computed from the 
observed elevation of the sun (m is unity for zenith 
position of the sun). If we assume a to have a given 
value, the only unknown quantities are /3 and F. The 
total selective absorption F has been expressed by 
Fowle through the linear equation 

F = 0.10 + 0.0054ecm, (3) 

where eo is the water-vapor pressure (mm Hg) at the 
surface of the earth, and m is the air mass. It is evident 
from several considerations that Fowle 's equation must 
include rather rough approximations. However, if we 
accept it as a first approach, it is evident that the 
quantity /j, which is a measure of the dust content, may 
be determined from equation (2) and a single pyrhelio- 
metric observation. In practice this determination is 
made by a graphical evaluation of the integral for 
various values of eo and ?n — made once and for all. The 
value of p which makes the value of the integral equal 
to the measured value of the radiation increased by 
F is then obtained from a diagram or from tables. We 
may effect the computation most simply by plotting 
the observed radiation, increased by F, on the diagram 
shown in Fig. 1 and interpolating the value of |8. 

We can, however, derive a similar result mote ac- 
curately if we add another pyrheliometric measure- 
ment to the one covering the total golar spectrum. By 
using a colored glass filter — RG 2 or OG 1 for instance — 
we can examine separately a part of the spectrum cover- 
ing all wave lengths longer than a given limiting value. 
The filter RG 2, for instance, lets through all radiation 
of wave lengths longer than about 0.6 n. With due 
regard to the nearly constant reflection (1 — 7) by the 
filter (where 7 is the fraction of incident radiation trans- 
mitted by the filter, that is, its transmission coefficient), 
we obtain for the observed filter radiation Qr, in per- 
fect analogy with equation (2), 



Qr = y I h^Hrn,l3,\)d\ - yF, 

•10.6 



(4) 



where 

4^ = 5'" exp (-/3m/X°). 

The value of F may here be assumed with good ap- 
proximation to be the same as in (2). Hence, from equa- 
tions (2) and (4), we obtain 



Qn.- -Qr = I loxi^dX - j loxi^dX, (5) 

7 Jo •'0.6 



f 



or 



1 /•"■« 

7 Jo 



(6) 



1. Given for instance in F. Linke, Meleorologisches Ta 1- 
huch, IV, Table 109, p. 2.38 (Akad. Verlagsges.) Leipzig, OTX^'. 

2. See F. Linke, Meleorologisches Taschenbuch, IV, Table 
113, p. 240. 



52 



RADIATION 



On the basis of this simple theory, the present author, 
and later Hoelper [6], Tryselius [11], and Olsson [8], 
among others, have computed values for /3 and the 
total selective absorption from simple pyrheliometric 
observations. 

This method for treating actinometric observations 
has been discussed in some detail because considerations 
in the foregoing discussion are apt to provide an answer 
to the question which follows. Suppose we wish to use 
the simple actinometric measurements of Qm and Q,- to 
obtain some idea of the scattering and absorbing prop- 
erties of the atmosphere (such a purpose is certainly an 
important justification for actinometric measurements 
in general), what is the accuracy that we should 
demand? It is perfectly clear from the simple theory 
presented here that, in order to make progress and ob- 
tain conclusions of importance, we are forced to intro- 
duce some simplifications in our assumptions concern- 
ing the laws governing atmospheric scattering. Such a 
simplification has been made in assuming a simple 
exponential expression for the dependence of the scat- 
tering on wave length. This simplification represents a 
rather rough approximation, and because of this there 
is very little use in attempting to determine values of 
i8 and a with an accuracy greater than about 5-10 per 
cent. This corresponds to accuracies in the values for 
the solar radiation Qm and Qr of about 1-2 per cent. For 
determinations of the scattering and absorption in the 
atmosphere by simple actinometric methods, this ap- 
pears to be the desirable accuracy.^ 

Actinometry with Regard to Biological Problems. 
The importance of solar radiation for a number of 
phenomena of biological character, such as plant growth 
and photosynthesis, and the health of man, has to a 
large extent led to the organization of actinometric 
measurements in connection with research concerning 
such phenomena. 

What accuracy is here required from the actinometric 
instruments? In trying to answer this question, we 
must keep certain facts in mind. It is evident that, in 
general, the radiation which we are able to measure or 
record is very seldom the radiation that is effective in 
the biological processes under investigation. Neither 
the radiation on a horizontal surface, recorded for in- 
stance by a pyranometer, nor on a spherical surface, 
nor on a surface perpendicular to the solar beam as in 
pyrheliometers, is equal or strictly proportional to the 
radiation falling on a given plant or other organism. 
Furthermore, it is seldom of much use to try to con- 
struct a perfect model of a plant or organism since the 
effectiveness of the radiation is, in general, quite dif- 
ferent at different parts of the plant's surface. In 



3. For a more detailed presentation of the methods for de- 
termining atmospheric turbidity on the basis of actinometric 
measurements along the lines indicated above, reference may 
nowJ->3 made to a valuable treatise by Dr. Walter Schtiepp, 
pijjjjj^ed after the present article was written: Die Bestim- 
mu>^ .ler Komponenten der atmospharischen Truhung aus Ak- 
tinometermessungen. Inaugural Dissertation, Wien, Springer, 
1949. 



addition, a number of other factors, of which as a rule 
we have a rather incomplete knowledge, are generally 
effective in producing the observed results on, for in- 
stance, photosynthesis or growth. Therefore, if we ask 
for the equipment which ought to be recommended for 
meteorological stations when we have biological or 
agricultural needs in mind, it seems more important 
that the instruments should be characterized by a 
certain simplicity and stability and that their results 
should be easily comparable with those from other 
stations, than that the instruments should be given some 
elaborate form in a rather vain attempt to imitate what 
can hardly be reproduced. Instruments which measure 
or record the radiation from the sun and sky on a hori- 
zontal surface and on a surface perpendicular to the 
solar beam thus seem to be able to satisfy more general 
needs. An accuracy of 5 per cent seems sufficient, 
provided that the instruments are not subject to sys- 
tematic errors or systematic changes. 

INSTRUMENTS AND MEASUREMENTS 

Determination of the Solar Constant for the Purpose 
of Ascertaining Its Variations. From what has been 
said above concerning the accuracy which must be 
demanded from the instruments for determining the 
solar constant, it must be concluded that none of the 
standard types of pyrheliometers in current use strictly 
satisfies these requirements. The two instruments which 
should be given first consideration are the compensa- 
tion pyrheliometer of K. Angstrom and the silver-disk 
pyrheliometer of the Smithsonian Institution (Abbot). 
Both have been subjected to rather elaborate investiga- 
tion and critical examination by various scientists and 
lately, in a very systematic way, by the International 
Radiation Commission. On the initiative of this Com- 
mission, Courvoisier [5] at the Observatory of Davos 
has made a complete theoretical survey of the principles 
of their construction, supplemented to some extent by 
experimental studies. 

With regard to the Angstrom compensation pyrheli- 
ometer, in the form in which it has been delivered by its 
manufacturers in Uppsala (Rose, now discontinued) and 
Stockholm (A. Lindblad), the following can be said 
of earlier as well as of more recent researches. 

As shown by the present author in 1914, the instru- 
ment is subject to a small error called the "edge effect" 
arising from certain features in its construction. The 
"edge effect" is caused by the fact that one of the strips 
which constitute the sensitive part of the instrument is 
heated electrically throughout its entire length, while 
the other strip is illuminated by the solar radiation only 
to about %o of its length on accoimt of the screening 
of a diaphragm inside the instrument. The error which 
thus arises is of the order of 2 per cent. It is, however, to 
some extent dependent on the convection in the air 
over the heated strips. Taking into account the condi- 
tions occurring in practice, we must conclude, from 
theoretical considerations supported by actual measure- 
ments, that the error arising from the edge effect may 
vary between the limits 2 ± 0.5 per cent. 



ACTINOMETRIC MEASUREMENTS 



53 



To obtain measurements for computing the solar 
constant Abbot has constructed a special Angstrom 
pjn-heliometer in which the edge effect is reduced to 
practicality zero. I-Iowe\'er, a detailed sur-\'ey of the 
factors influencing measurements with this type of 
instrument leads one to conclude that errors of the 
order of ±0.3 per cent can hardl3'^ be avoided completely. 

The silver-disk pyrheliometer has been extensively 
used, especially in connection with Abbot's earlier work 
on the solar constant. Courvoisier has subjected it to a 
very thorough theoretical examination, with due regard 
to the physical constants of the instrument. Some minor 
corrections must be applied to Abbot's theory on which 
the method of measurement is founded. These correc- 
tions may affect the absolute values obtained. What 
interests us here especially are the variable errors aris- 
ing from the variation of different physical and me- 
teorological factors. Strictly speaking, Abbot's theory 
holds true only when the instrument is maintained at 
semiconstant temperature during the periodical tem- 
perature variation to which it is subjected when alter- 
nately exposed to and screened from solar radiation. 
This puts a rather high demand on the precautions to 
be taken during e.xposure. 

Further effects arise from the unavoidable fluctua- 
tions of the temperature of the surrounding air, which 
in turn affect the temperature of the cylindrical wooden 
cover by which the silver disk is protected. Courvoisier 
concludes that errors up to 0.3 per cent are possible on 
that account. Morikofer [7] estimates the average error 
from various causes to be about 0.5 to 1.0 per cent. 

Among the instruments rather widely used, the 
Michelson actinometer is especially convenient, since 
it is rapidly read and does not require auxiliary instru- 
ments. Its accuracy is less than that of the Angstrom 
or the silver-disk instruments, the average error prob- 
ably amounting to ±1.0-1.5 per cent. The Michelson 
actinometer should be checked at regular intervals 
since it is sometimes subject to deterioration. As the 
accuracy of the instrument seems sufficient for general 
meteorological pui'poses, it would be highly desirable 
that instruments of a similar construction should be 
built in greater number and at moderate cost. 

Small differences exist between the indications of all 
actinometers in practical use for measuring direct solar 
radiation. They arise from the fact that the instruments 
receive not only direct solar radiation but also diffuse 
radiation from the sky in the immediate neighborhood 
of the sun, within certain aperture angles which vary 
with the instrument. Thus the silver-disk pyrheliometer 
has an aperture of 6° (formerly 10.5"), while the Ang- 
strom compensation pyrheliometer has a rectangular 
aperture with plane angles of 24° and 6° (more recently 
10° and 3°), respectively. The Angstrom instrument 
consequently receives in general somewhat more scat- 
tered light, and the difference between the readings of 
the Angstrom (A) and the silver-disk {S) instruments 
can be approximately expressed by 

A - S = ~ A+ f{q, (3, a, m), (7) 

where A is the difference which is to be expected at the 



limit of the atmosphere where no diffuse radiation is 
added to the direct radiation, and / (g, /3, a, m) is a 
function of the quantities g, etc. (notation as given 
earlier). The function/ (g, fi, a, m) is equal to zero when 
g equals unity and /3 vanishes. According to experience 
recently acquired, this function seems to vary, at 
stations near sea level, between about 0.01 cal cm~^ 
min~^ for low values of B to about 0.02 cal cm~^ min~i 

' o 

for high values of )3. The difference S — A therefore 
seems to vary between about 1.5 and 4.0 per cent, 
where the upper and lower limits correspond to extreme 
conditions (Angstrom — uncorrected for edge effect; sil- 
ver-disk — Smithsonian scale, 1934). 

With due regard to recent investigations, we may, 
chiefly according to Morikofer [7], give the following sur- 
vey on the status of absolute actinometry. Setting 
the indication of the Angstrom pyrheliometer equal to 
100 per cent, we have: 

Instrument Per cent 

Angstrom (uncorrected) 100.0 

Angstrom (corrected for edge effect) 101.3 ±0.5 

Smithsonian scale, 1913 103.5 

Solar Radiation Commissions (preliminary re- 
sults) 1936 (see [3]) '. . . . 101.0 

Guild, Physical Laboratory, 1934 101.3 

Abbot (Smithsonian scale, 1934) 101.2 

Actinometric Equipment at Meteorological Stations. 
It would be futile to attempt actinometric measure- 
ments, even at selected meteorological stations, for 
the purpose of computing the solar constant, and still 
more so for determining its possible variations. The 
required elaborateness and quality of the actinometric 
equipment are such that measurements for this purpose 
must be reserved for observatories with very high 
standards, at locations carefully selected with regard 
to atmospheric conditions. 

On the other hand, the chief problems which actino- 
metric observations from a meteorological network 
might help to solve are those which we have briefly 
discussed in the first section of this article. Thus, the 
measurements should (1) furnish data for an evaluation 
of the heat exchange at the surface of the earth and 
enable us to treat, on this basis, the fundamental prob- 
lem of the energy transport within the atmosphere; 
(2) provide the means for a general optical analysis of 
absorption and scattering in the atmosphere; and (3) 
furnish the basis for correlation studies of the relation- 
ship between the radiation processes at the earth's 
surface and a number of biological phenomena such 
as the growth of plants, crop conditions, the health of 
man, and the incidence and spread of certain di.seases. 

It is clear from what has been said above that the 
accuracy required of our actinometric equipment for 
these purposes is much less than that for the determina- 
tion of the solar constant. The accuracy and case of 
operation of our present instruments are undoubtedly 
satisfactory for these general purposes. 

The details of the organization must be based on a 
realization of the main problems, on experience or 
knowledge, otherwise gained, concerning actinometric 
instruments and their qualities, and finally on some 
acquaintance with meteorological obser\'ations in gen- 



54 



RADIATION 



eral and with what can reasonably be demanded from 
the observers. On the basis of such considerations the 
following general pattern for the actinometric stations 
within a meteorological network is recommended. The 
proposed organization is based partly on the author's 
o^vn experience, but is, to a very large extent, the result 
of discussions with colleagues. 

Central Actinometric Observatory (fJAO). It seems de- 
sirable that at least one such observatory should be 
established within every large country. Among its main 
objectives would be scientific investigations of actino- 
metric problems of a geophysical character, or those 
with geophysical applications. A plan for such investi- 
gations will not be discussed here, since it must be 
based chiefly on the personal initiative and scientific 
ideas of the observatory personnel. Among the prob- 
lems deserving general attention are especially the dis- 
tribution of ozone and its determination by actino- 
metric methods and also special investigations of 
ultraviolet radiation. The former problem is at present 
being vigorously pursued by G. M. B. Dobson at Ox- 
ford, and it seems probable that in the near future his 
investigations will result in the construction of appara- 
tus which can be generally accepted for ozone measure- 
ments. The work at the Bureau of Standards by W. 
Coblentz and later by R. Stair and his collaborators 
will probably lead to similar results with respect to the 
measurement of ultraviolet radiation. 

First we shall discuss the relation which should exist 
between the activities of the central actinometric ob- 
servatory and the actinometric stations of the mete- 
orological network, as they will be described below. The 
CAO must form a center for calibration, standardiza- 
tion, and checking of secondary instruments, and for 
this purpose such a central observatory should be 
equipped with absolute instruments. The actinom- 
eter perhaps most widely used for measuring direct 
solar radiation, the Michelson actinometer, is a second- 
ary instrument and, because of a certain delicacy in its 
construction, it seems desirable that it be compared 
at regular intervals with an absolute instrument or at 
least with other instruments of greater stability. The 
silver-disk pyrheliometer of the Smithsonian Institu- 
tion is also a secondary instrument. Its construction is 
much less delicate than that of the Michelson actinom- 
eter, and in several instances the instrument has 
retained its calibration unchanged during rather long 
periods. However, as a precaution against error, if the 
instrument is to be used daily, it should be compared 
from time to time with an absolute instrument or a 
secondary standard, preferably at least once a year. 

The Angstrom compensation pyrheliometer is strictly 
an absolute instrument. Its "constant," which is ap- 
plied to the direct reading in order to yield the cor- 
responding radiation values, can be determined through 
simple physical measurements of resistance, dimensions, 
etc., on the instrument. But in practice such measure- 
ments are very seldom made, and they can hardly be 
carried out without rather elaborate physical equip- 
ment. Therefore, the instrument is actually used at 
most stations simply as a secondary instrument relying 



upon the correctness of a standardization carried out 
prior to delivery of the instrument. It is clear, especially 
since the construction is rather delicate, that reliance 
on a single calibration involves the serious risks of 
collecting observational data of greatly reduced value. 
For this reason, a standardization, either through com- 
parison with a central standard or through a physical 
determination of the constants of the compensation 
pyrheliometer, should be carried out at regular inter- 
vals. A central actinometric observatory would be the 
proper place for that purpose. 

Second Order Actinometric Stations. Provided that 
absolute standardizations are carried out at a central 
observatory, second order stations do not need to be 
provided with absolute instruments. On the other hand, 
it seems advisable that they be furnished with double 
sets of actinometers for measuring direct solar radia- 
tion, in order that one instrument can, to some extent, 
serve as a check on the other. The following measure- 
ments are proposed. 

1. Measurements of the direct total solar radiation 
at least three times a day when the sky is clear. 

Instruments: Smithsonian silver-disk pyrheliometer, 
Angstrom compensation pyrheliometer, or an instru- 
ment of the Michelson type. These are the instruments 
which have been most carefully examined with respect 
to various errors. However, other instruments may also 
be used, provided they are carefully standardized. 

2. Measurements of direct solar radiation within 
special regions of the spectrum with the aid of colored 
glass filters of the type RG 2 or OG 1, through which 
the infrared radiation may be separated from the visible 
and ultraviolet (at least three times a day with a clear 
sky). 

Instruments: Same as under 1. 

3. Continuous measurements of the total incoming 
radiation from the sun and sky. 

Instruments: Moll-Gorczynski actinograph with re- 
cording galvanometer, Kimball-Eppley actinograph, 
Angstrom pyranometer with photographic recorder, Ro- 
bitzsch actinograph, or instruments of similar construc- 
tion. 

Screening these instruments from direct solar radia- 
tion and comparing the reduction of their reading with 
the direct solar radiation, measured simultaneously, 
provides a check on these recording instruments. With 
this method, the first three instruments mentioned 
above will easily yield results accurate to about ±5 
per cent for individual days and ±3 per cent for longer 
periods. 

With regard to the Robitzsch actinograph, the con- 
struction of which is similar to a common thermograph 
with bimetallic elements, the following remarks may 
be made. The instrumental "constant" (the factor by 
which the deflection on the recording drum must be 
multiplied in order to give radiation values) is highly 
dependent on temperature. A temperature rise of one 
centigrade degree generally corresponds to an increase 
in the constant of about 1 per cent. Furthermore, the 
sensitivity is to some extent dependent on the elevation ' 
of the sun as well as on the orientation of the instrument 



ACTINOMETRIC MEASUREMENTS 



55 



relative to the sun. Most important in the use of the 
instrument is a careful examination of its dependence 
on temperature. Under all circumstances, rather fre- 
quent comparisons with actinometers for solar radia- 
tion measurements must be made. It is difficult to 
avoid errors of less than about ±10 per cent for in- 
dividual days and less than ±5 per cent in monthly 
means. 

4. Measurements of the outgoing "effective" radia- 
tion. 

o 

Instruments: Angstrom pyrgeometer with electrical 
compensation. Some of the errors inherent in this in- 
strument are the same as for the compensation pyr- 
heliometer. A variable edge effect introduces errors up 
to about ±3 per cent in single measurements. No 
recording device of suitable design can yet be recom- 
mended for general use. Some theoretical investigations 
by Prohaska and Wierzejewski [9] on the Bellani instru- 
ment for measuring incoming radiation seem to support 
the view that the Angstrom "tulipan" instrument 
founded on a similar principle, that is, overdistillation 
of ether under the influence of outgoing heat radiation, 
may adequately serve its purpose of performing time 
integration of "effective" radiation. The necessary pre- 
cautions seem, however, to be too mmierous to allow a 
more general use. 

5. Records of hours of sunshine. It is recommended 
that the duration of sunshine be recorded at all stations 
where the total radiation from sun and sky is recorded. 
Special studies of the relationship between the duration 
of sunshine and the incoming radiation at various 
stations will then provide a possibility of computing 
the incoming radiation from the hours of sunshine 
Qs according to some formula, for instance, Qs = 
Qo[a -f (1 — a)S], where the constants Qo and a must 
be determined. Such studies may give us a means of 
interpolating radiation values for localities between ac- 
tinometric stations from the number of hours of sun- 
shine recorded at a much larger number of places. 

Instruments: Most widely used are the sunshine 
recorders of Campbell-Stokes and the recording black- 
bulb thermometer used by the United States Weather 
Bureau. It should be emphasized that these instruments 
can under no circumstances be considered as instru- 
ments of precision. It is more important to correlate 
the data from the various types of sunshine recorders 
with the radiation balance than to attempt to stand- 
ardize or correct the instruments so that a precise 
measurement of the loosely defined "hours of sunshine" 
may be obtained. With this guiding principle in mind, 
one may allow rather wide variations in the type of 
instrument. 

Third Order Actinometric Stations. These stations 
should be equipped with sunshine recorders as well as 
with simple recording instruments such as the MoU- 
Gorczynski, Kimball-Eppley, or the Robitzsch type. 
The pyranometers should, however, be checked at regu- 
lar intervals by comparison with secondary standard 
actinometers, either brought to the stations during 
inspection or kept at the station for use on special 



occasions. The frequency of these check measurements 
must, to some extent, be chosen on the basis of ex- 
perience concerning the constancy of the recording 
device, which probably depends on the climate. 

Regular Meteorological Stations Equipped with Sun- 
shine Recorders. In general, it seems advisable that all 
actinometric stations of the second and third orders 
should also be meteorological stations of at least the 
second order. This will facilitate studies of the relation 
between radiation and other meteorological elements. 

A rather wide network of stations recording simply 
sunshine duration is desirable so that they may act as 
interpolation stations with respect to the radiation 
balance. However, it is also recommended that other 
meteorological observations be made at such stations, 
at least observations of cloudiness, temperature, and 
precipitation. 

CONCLUSIONS 

Critique of Routine Actinometric Measurements as 
Hitherto Organized. It is generally realized that actino- 
metric measurements are still in a state in which an 
organization according to systematic and generally ac- 
cepted rules is lacking. The observations are, as a rule, 
limited to certain single observatories, and there is, in 
general, no possibility for a synoptic treatment of the 
results. Only very seldom are the observations made in 
a manner which permits separation of scattering and 
absorption in the atmosphere. 

The recording devices, such as the MoU-Gorczynski 
instrument or the Robitzsch instrument, when used 
at field stations, are in many cases too infrequently 
checked, a fact which especially for the latter instru- 
ment is rather fatal, since its indications are highly 
dependent on the manner of exposure, and its constant 
is highly variable with temperature. Many obser- 
vational data of no value have been collected in this 
way. 

Measurements of the effective radiation, important 
as they may seem, are almost totally lacking, with the 
exception of the results from only a few observatories. 
Regular checks of the instruments in use are seldom 
made. 

It is my opinion that our knowledge and experience 
of the instruments available are such, after the work 
on the subject particularly by the Smithsonian Institu- 
tion and the International Radiation Commission in 
close collaboration with the Observatory of Davos, 
that the time is ripe for a systematic organization of an 
international actinometric station network within the 
meteorological organization. The technical and instru- 
mental problems which still need to be solved and the 
improvements to be expected need not delay an organi- 
zation which now seems highly desirable. 

Special Problems. We have already briefly indicated 
the problems which such an actinometric network would 
primarily help to solve. They include the important 
problem concerning the energy exchange within the 
earth's atmosphere and the factors influencing it. If we 
consider a given vertical column extending from the 



56 



RADIATION 



earth's surface to the upper limit of the atmosphere, the 
temperature of the air within this column is determined 
primarily by the incoming and outgoing radiation, by 
the transfer of energy through horizontal advection, 
and, to some extent, by evaporation and condensation 
processes. If we take a column of a sufficiently large 
cross section and consider a sufficiently long time inter- 
val, our problem of analyzing the factors influencing 
the temperature coincides with the problem of finding 
the causes for climatological temperature changes in 
general. Here, incoming and outgoing radiation are the 
most fundamental elements. Without a thorough knowl- 
edge of these factors, their distribution and variations, 
all speculations on climatic variations are reduced to 
rather vague guesses. 

Another equally important problem, closely con- 
nected with the climatic variations, concerns the trans- 
mission of the atmosphere and its fluctuations. A clear 

















0.12 
0.10 
0.08 
0.06 
0.01 
0.02 








/ 


^ 


X 








/ 












/ 










_^ 










v__ 



























90° 
S 



60° 



30° 



0° 30° 

LATITUDE 



60° 



90° 
N 



Fig. 2.— Preliminarjr curve showing variation of scattering 
coefficient /3 with latitude. 

separation between scattering and absorption is neces- 
sary. The simplest way of accomplishing this is indi- 
cated above. If we take the coefficient /3 as a measure of 
the scattering of the atmosphere, the following remarks 
may be made. A rather summary treatment of avail- 
able pyrheliometric data already shows that /3 is on the 
whole much larger in tropical and subtropical regions 
than at higher latitudes. The graphical representation 
in Fig. 2, taken from a previous paper by the author 
[2], shows this, but it maybe taken only as a very rough 
indication of the general conditions. More extensive 
observational data, systematically treated, must be 
available before the distribution of /3 over the whole 
globe can be mapped. Intensive investigations may 
here solve the problem concerning the dust-producing 
centers at the earth's surface, the nature of the scatter- 
ing particles, and their origin under various conditions. 
Investigations near desert regions seem to show that 
the scattering particles directly produced by storms 
over the desert are much larger than those which 
generally occur in the atmosphere. At all Northern 



Hemisphere stations investigated for an annual varia- 
tion of /3, the scattering coefficient reaches a pronounced 
maximum in the spring (April or May). The values of 
^ obtained at Spitsbergen by Olsson [8] and at Abisko 
(northern Lapland) by Tryselius [11] are so low that 
the scattering there must be almost totally due to the 
molecules. Therefore, if we consider only the effect of 
scattering, the ultraviolet radiation at, for instance, 
30° solar elevation in Lapland, must be almost as in- 
tense as at about 2000-m height in Switzerland for the 
same solar elevation. Only a few of the problems re- 
lated to a more detailed synoptic investigation of scat- 
tering in the atmosphere have been indicated here. 

The outgoing "effective radiation" should be the 
object of a closer investigation especially with respect 
to its distribution over the earth's surface. In general, 
it seems to be very closely related to two factors: (1) 
the temperature at the place of observation and the 
temperature distribution in the atmosphere, and (2) 
the content of water vapor in the atmosphere. This rela- 
tionship is so close that it is doubtful whether there 
are any other factors whose effects do not fall within 
the errors of observation. On the other hand, there are 
some indications of a variation during the night, which 
might not be explained by a variation of the previously 
mentioned elements. Here is an important field of 
research from which perhaps some factor influencing the 
climatic variations may be discovered. 

Finally, for the important studies of the relation 
between biological phenomena and radiation, an actino- 
metric network has an essential task to fulfill. In all 
these studies in which special portions of the spectrum 
must be considered effective, a clear separation between 
scattering and absorption is necessary. When we know 
the scattering coefficient and its variations, we will be 
able to give a much more detailed picture of the varia- 
tions in the different spectral regions of the sun's 
radiation. Such a detailed knowledge is probably neces- 
sary before the relation between biological pheno- 
mena and solar radiation can be investigated with 
success. 

REFERENCES 

1. Angstkom, a., "On the Atmospheric Transmission of 
Sun Radiation and on Dust in the Air." Geogr. Ann., 
Stockh., 11:156-166 (1929). 

2. "On the Atmospheric Transmission of Sun Radiation, 

II." Ibid., 12:130-159 (1930). 

3. "Survey of the Activities of the Radiation Commis- 
sions of the International Meteorological Organisation 
and of the International Union of Geodesy and Geo- 
physics." Tellus, Vol. 1, No. 3, pp. 65-71 (1949). 

4. "Atmospheric Circulation, Climatic Variations and 

Continentality of Climate" in Glaciers and Climate 
(Geophysical and geomorphological essays dedicated to 
Hans W;son Ahlmann). Geogr. Ann., Stockh., Vol.31, 
Nos. 1 and 2, pp. 316-320 (1949) . 

5. CouEvoisiER, P., und Wiebzejbwski, H., "Beitrage zur 

Strahlungsmessmethodik. I — Die phj'sikalischen Grund- 
lagen der kalorischen Strahlungsmessmethoden." Arch. 
Meteor. Geophys. Biokl., (B) 1:45-53 (1948). "II— Die 



ACTINOMETRIC MEASUREMENTS 



57 



Bei'echnung der Wirkungsweise kalorischer Strahluiigs- 
messinstrumente."/6fc;., (B) 1:156-199 (1949). 

6. HoELPEK, O., "Der atmospharische Triibungszustaud iiber 

Aachen nach kalorischen Strahluugsmessungen im Polar- 
jahr." Dlsch. meteor. Jb. Aachen (1933). Aachen, 1935. 

7. MoRiKOFER, W., "Meteorologische Strahlungsmessmetho- 

den." Handb. biol. ArbMelh., E. Aberh.\lden, Hsgbr., 
2.4005-4245 (1939). 
S. Olsson, H., "Meteorological Observations at Mt. Norden- 
skiold, Spitzbergen, during the International Polar Year, 



1932-33." Medd. meleor.-hydr. Anst., Stochh., Vol. 6, 
No. 5, 83 pp. (1936). 
9. Prohaska, F., et WiERZE.rEWSKi, H., "Th^orie et pratique 
du pja-anoraetre sph(5rique de Bellani." Ann. Geophys., 
3:184-221 (1947). 

10. ScHMOLiNSKY, F., "DieWellenlangenabhangigkeit der Sicht- 

weite und des Koeffizieuten der Dunstextinktion." Me- 
teor. Z., 61:199-203 (1944). 

11. Trysblius, O., "On the Turbidity of Polar Air." Medd. 

meteor. -hydr. Anst., Siockh., Vol. 5, No. 7, 10 pp. (1936). 



METEOROLOGICAL OPTICS 

General Meteorological Optics by Hans Neuberger 6l 

Polarization of Skylight by Zden'ek Sekera 79 

Visibility in Meteorology by W. E. Knowles Middleton 91 



GENERAL METEOROLOGICAL OPTICS 

By HANS NEUBERGER 
The Pennsylvania State College 



The phenomena of meteorological optics are not as 
generally well known as those of other branches of 
meteorology. For this reason, the subsequent sections 
are introduced with a brief description of the major 
phenomena and a summarj^ of known facts. For ab- 
normal variations the reader is referred to the multi- 
tude of meteorological, astronomical, and general 
science periodicals. Visible sound waves in the sky, 
frequently observed during World War 11,^ could not 
be considered here. 

In order to keep the number of references within 
space limits, authors whose contributions have been 
discussed in standard works are, where possible without 
ambiguity, cited from these works; this is indicated by 
a "c" preceding the respective reference number. 

SUBJECTIVE PHENOMENA IN THE 
ATMOSPHERE 

The Apparent Shape of the Sky. When scanning the 
daytime sky, an observer perceives a more or less 
flattened vault. For some observers, this impression 
persists even at night, although the multitude of stars 
in their different magnitudes tends to convey the idea of 
a rather undefinable space. The variety of impressions 
is the result of a complex psychometric coordination of 
the visual and the physical space. This coordination is 
not a simple transformation of a geometric reality such 
as obtains for an overcast sky, because, in the case of 
the clear daytime sky, we look into an indefinite depth 
of the luminous atmosphere. Indeed, if we fix our sight 
in any elevated direction, we fail to perceive a "surface" 
on which our eyes may rest. However, if we let our 
eyes wander between zenith and horizon, the impression 
of such a surface is inescapable. The problem of the sky 
shape, although some of its aspects lie within the realm 
of psychophysics, is of meteorological interest because 
of its bearing on the practice of estimating cloudiness. 

Smith [c. 42] introduced a method by which a numeri- 
cal value can be assigned to the apparent flatness of the 
sky, by measuring the elevation angle a (Fig. 1) of the 




Fig. 1. 



-Half-arc angle a as a measure of the apparent shape 
of the sky. 



estimated position of point M that bisects the imagi- 

1. For example, see W. E. K. Middleton, .7. R. aslr. Soc. 
Can., 38: 432 (1944). 



nary arc ZH from zenith to horizon. The half-arc angle 
a is then a measure of the flatness of the sky, becoming 
smaller as the sky appears flatter. Another method for 
expressing the sky flatness numerically is the estima- 
tion of the ratio of the apparent distances OH/OZ, 
which increases with increasing flatness of the sky. 
The estimation of this ratio is a more difficult task than 
bisecting the arc ZH and is a much coarser measure. 
Assuming, for example, a circular sky profile, we can 
compute corresponding values of OH/OZ and a [c. 42]; 
OH/OZ = 1, 2, 3, 4, corresponds to a = 45°, 33°, 25°, 
20°, respectively. Since most observations fall in the 
range 20° < a < 40° and are reproducible within 1°, 
while OH/OZ can be estimated, at best, only in whole 
numbers, OH/OZ is obviously an inadequate measure. 

Various authors have deduced the curvature of the 
sky profile as circular, elliptic, parabolic, hyperbolic, or 
helmet-shaped [8, 9, 22, 23, c. 42]. The angle at which 
the sky appears to meet the horizon plane is one 
criterion of the geometric form. This angle would be 90° 
only in the cases of elliptic and parabolic shapes, but 
more or less acute in all others. A parabolic profile would 
also be distinguished by the pointed appearance of the 
zenith sky. Another criterion is derived from compari- 
son of observed overestimation of elevation angles of 
objects with those computed under the assumption of 
various sky shapes [42]. Variations of a psj^chological 
nature among different observers and physical varia- 
tions of sky conditions undoubtedly preclude the as- 
sumption of any unique sky shape. For the discussion 
of observational results, consideration of the half-arc 
angle a may suffice. 

Table I shows the effect of general sky brightness and 
cloudiness on the depression of the sky as seen by vari- 
ous observers. Although the large differences among 



Table I. Average Half-Arc Angles for Various 
Sky Conditions 



Observer 



Dember and Uibe [8]. 

Miller [37] 

Reimann [c. 42] 

Mendelssohn and Dem 
ber [33] 



Daytime 



cloudy clear 



29.0° 

29.9 

21.0 



32.0° 

34.0 

22.5 

31.9 



Twilight 
clear 



32.2° 



Clear night 



moonlit moonless 



36.7° 

26.6 

36.6 



40.1° 
30.0 



observers reflect the strong subjectivity of the phe- 
nomenon, the same trend appears in the effect of the 
^'arious sky conditions. The cloudy daytime sky looks 
flattest, the moonless night sky most arched. Some of 
the individual differences may be due to effects of 
locality, since the observations cited were made at 
different places and altitudes. 



61 



62 



METEOROLOGICAL OPTICS 



The effect of the amount of cloudiness is demon- 
strated in Table II by the most recent observations 
[37]. In qualitative agreement with observations by Rei- 
mann [c. 42], these data show that even a few clouds in 
the sky materially increase its apparent flatness, whereas 
with sky covers of > %o, the observer refers chiefly 



Table II. Average Half-Arc Angle for Various 
OF Cloudiness 


Steps 


Clouds tenths 





<1 


1-3 


4-7 


8-9 


>9 


a n 


34.0 


32.6 


31.5 


30.6 


30.2 


29.9 



to the cloud layer in forming his impression of the sky 
shape. Therefore, for cloudiness > Mo> the increase 
in flatness becomes practically negligible. 

Miller [37, 38] seems to be the only observer to investi- 
gate the effect of cloud types (and ceiling height) on the 
apparent sky shape. Table III shows his results for 
various cloud types arranged in order of increasing 
average cloudiness for these types. The groups Ac and 
As,'^ and Sc make the sky appear flatter than would 
result from the implicit cloudiness effect. This has been 
attributed to the structure of the underside of Ac and 
Sc, which facilitates depth perception and makes the 
observer aware of the extension of these cloud layers 
beyond the terrestrial horizon. This apparent increase 
of the horizontal extent of the cloud layers causes a 
decrease in a. 

Table III. Relationship between Cloud Type and 
Half-Arc Angle 



Cloud type 


Average cloudiness, tenths 


Average «{") 


Cu, Fc 
Ci, Cs 
Ac, As 
Sc 
St 


4 
5 
7 
8 
10 


30.0 
29.1 
27.8 
28.4 
29.0 



From Table III it is also obvious that the cloud 
height does not influence the apparent flatness of the 
sky, in the manner which might be expected from 




Fig. 2. — Geometric relation between cloud height and half -arc 
angle. 

purely geometric considerations (Fig. 2). The Ac- and 
.4s-group, for example, is associated with a smaller a 

2. Ac and As occurred simultaneously in almost all cases. 



than is the (S^group, whereas the reverse should be true 
according to Fig. 2 if the visual space were a simple 
transformation of the physical space. A comparison 
between Table III and the last three columns of Table 
II shows that the type of clouds has a greater effect than 
the amount of clouds. 

In contrast to Dember and Uibe [9], Miller [37] found 
that the visual range has only a minor influence on the 
apparent shape of the sky, whereas the effect of the 
distance to the terrestrial horizon is very strong, as 
shown in Table IV. The differences in a between various 

Table IV. Average Effects op Visual Range (V) and 
Horizon Distance (D) on the Half-Arc Angle (a) 



V (km) 


I> = 0.4 km aC) 


D = 12kma(°) 


<6 

6-10 

>10 


33.3 
32.1 
32.6 


30.7 
28.8 
28.9 


Mean 


32.6 


29.2 



groups of visual range are considerably smaller than 
between different horizon distances. This result was 
confirmed by measurements of a at various distances 
from a mountain range [38]. In addition to the actual 
distance of the horizon, the facilities for subconscious 
estimation of this distance, such as is offered by suitable 
foreground configuration, have also proven of strong 
influence on the perceived sky shape [23, 37, 38]. For 
this reason, the sky dome cannot generally be considered 
a rotational geometric figure. 

Related Phenomena. Closely related to the shape of 
the sky is the well-known enlargement of sun or moon 
when near the horizon [23, 42]. As can be seen from the 
shaded angles in Fig. 3, the same angular subtense in- 
tersects a greater portion of the flattened sky near the 




Fig. 3. — Relationship between true and apparent (slanted 
numbers) elevation angles and angles of subtense (bracketed 
numbers) . 

horizon than at higher elevations, and this portion be- 
comes greater as the sky becomes flatter. The same 
holds true for the angular distance between stars. Jef- 
freys [25] raised an objection to this projection theory 
on the grounds that the sun or moon should appear 
elliptical with a long vertical axis, because only this 
axis would be distorted by the shape of the sky. How- 
ever, the angular subtense is too small to permit de- 
tection of such a deformation; moreover, this effect is 
probably compensated by an opposite effect of the 



GENERAL METEOROLOGICAL OPTICS 



63 



physical distortion owing to astronomical refraction. The 
size variation can also be explained by the general 
overestimation of angular elevations of terrestrial and 
celestial objects. On the left side of Fig. 3 the flat arc 
of the sky is divided into six equal segments correspond- 
ing to 15°-intervals of estimated elevations (slant num- 
bers). The true elevations show by comparison that 
the relative overestimation is > 100 per cent for small 
elevation angles and decreases to zero at 90°. The abso- 
lute overestimation reaches a maximum at true eleva- 
tions between 30° and 40° [23, 42]. The right side of Fig. 
3, showing true 15°-intervals and their estimated equiv- 
alents (in brackets), indicates that a given angular 
subtense is overestimated when below roughly 30° ele- 
vation, underestimated w^hen above 30°. Accordingly, 
the M° - subtense of sun or moon appears larger near 
the horizon, smaller at higher elevations. 

The overestimated height and steepness of moun- 
tains [22, 42] and the apparent ellipticity of circular 
halos [23, 34] are also related to this phenomenon, as 
is the incorrect estimation of the amount of clouds. The 
latter is of practical significance, because an observer 
tends to underestimate the amount of clouds overhead 
and to overestimate the amount of clouds near the 
horizon. This fact is qualitatively known, and in the 
observer's manual, measurements of angular elevations 
of clouds are suggested to eliminate this error for ad- 
vancing or receding cloud layers and those surroimd- 
ing the station. However, no such expedient is avail- 
able for estimations of the more frequent nonuniform 
states of sky. This problem can be summarized as fol- 
lows: The estimates of cloud covers of and 10 tenths 
are usually correct. For all other cloud amounts, the 
error made by the observer is a function of subjective 
factors (experience, etc.), of the amount and type of 
the clouds, the distance of the terrestrial horizon, and 
the general brightness level (Tables I-IV). 

Theories and Problems. All attempts to formulate 
an all-inclusive theory of the apparent shape of the sky 
have thus far been unsuccessful, chiefly because of the 
simultaneous involvement of physical and psychophysi- 
ological factors. Although physical and geometrical vari- 
ables modify our impression of the sky shape, they do 
not suffice, in themselves, to explain the observed facts. 
The simple consideration of the geometric properties 
of a cloud layer at 2000 m, for example, w^ould result in 
an a = 1°, whereas a. is actually observed between 20° 
and 30°, that is, the sky does not appear as flat as it 
should. A similar discrepancy arises for the clear sky 
[38]. From a physical standpoint, Dember and Uibe [9] 
attribute the sky shape to the distribution of sky bright- 
ness. They assume that the maximum distance from 
which scattered light reaches the observer is propor- 
tional to the square root of brightness. However, their 
theory not only implies that the brighter objects appear 
to be farther away, w^hich is not true [42] {e.g., brighter 
stars appear nearer), but also precludes any variations 
of the sky shape with the distance of the terrestrial 
horizon. Similarly, Humphreys [21] believes that the 
greater haziness near the horizon produces the impres- 
sion of greater distance than is the case at more elevated 



regions of the sky. While this effect is undoubtedly 
present, its magnitude has been shown in Table IV to 
be of secondary order only. Purely psychophysiological 
explanations are similarly unsatisfactory. Gauss and 
others [c. 42] were of the opinion that, because our line 
of sight is habitually horizontal and normal to the body 
axis, the illusion of a variable moon size should disap- 
pear when the direction of sight is changed by mirrors 
or the body orientation altered. Not aU results of perti- 
nent experiments supported this theory. Also, the ef- 
fects of physical variables would remain unexplained. 
Various attempts at a combination of geometric and 
psychophysical explanations have also been made. For 
example, v. Sterneck based his transformation of physi- 
cal into visual space on the underestimation of dis- 
tances according to a hyperbofic function, while Witte 
assumed that a straight line in physical space also ap- 
pears rectilinear in visual space [c. 42]. According to 
Exner [42], the moon's visible area is compared to that 
of the fovea when the moon is high, but at low moon the 
respective linear dimensions are compared because of 
the attention conamanded by the horizon line. This 
hypothesis, however, is incapable of explaining the sky 
shape or the variations in the moon's apparent size 
caused by external physical factors. Isimaru [23] com- 
bined, in his theory of the shape of the cloudy sky, the 
underestimation of distances with the overestimation 
of elevation angles. The same idea was foUowed by 
Hiittenhain [22] who reverted to v. Sterneck's theory. 
Both authors [22, 23] make the implicit assumption 
that the overestimation of angular elevations is in- 
dependent of the sky shape, because it can also be ob- 
served in rooms [22]. However, since both phenomena 
are due to the properties of our visual space, they can- 
not be independent. 

Fundamentally, all of the theoretical approaches to 
the general problem have hitherto been based on the 
assumption that the visual space is Euclidean and can 
be obtained by some unique transformation of the 
three-dimensional manifold of the physical space. How- 
ever, Luneburg [30] has recently shown that the sensa- 
tions produced by binocular vision represent a Rie- 
mannian manifold. From the analysis of certain optical 
illusions he concluded that the geometry of our visual 
space is the hyperbolic geometry of Lobachevsld as 
had already been indicated by Slvreb [49]. With this 
theory a differential equation for the apparent size of 
a line element in the horizontal plane was developed, 
which is, however, not immediately applicable to the 
problem of the apparent shape of the sky; at any rate, 
an extension of this theory to include this group of 
phenomena appears desirable. The major physical fac- 
tors whose effects must be explained by such a theory 
may be tabulated as follows: 

1. General brightness of the visual field and bright- 
ness distribution over the sky. 

2. Cloud types and amounts. 

3. Distance of terrestrial horizon, and facilities for 
estimating this distance. 

In addition, there are several phases of the problem 
that have been insufficiently explored or are entirely 



64 



METEOROLOGICAL OPTICS 



unknown as yet. For example, the practical problem 
of the mutual influence of sky shape and cloudiness es- 
timation needs further exploration. Simultaneous photo- 
graphic records of the sky, estimation of cloudiness, 
and determination of the shape of the sky (under all 
possible states of sky) may furnish an individual cor- 
rection factor for adjustment of cloudiness estimates. 
In particular, the quality of cloudiness estimations for 
individual cloud layers in the presence of other cloud 
decks needs special attention, as does the effect of the 
configuration of the terrestrial horizon on such estima- 
tions. More observations are also needed on the follow- 
ing effects: possible seasonal variations; the terrestrial 
horizon distance in conjunction with the configuration 
of the visual field between horizon and observer; the 
measured brightness level and brightness distribution 
over the sky. 

Wholly unexplored is the possible effect of an observ- 
er's altitude above the earth's surface on his impression 
of the sky shape and consequently the accuracy of his 
cloudiness estimation; this phase is especially of in- 
terest for meteorological observers on mountains or in 
airplanes. In this connection, the apparent shapes of 
the terrestrial surface and of cloud layers, as seen from 
above, deserve attention, because the quality of es- 
timations of cloudiness below an aerial observer hinges 
on this problem. 

REFRACTION PHENOMENA IN THE 
CLOUD-FREE ATMOSPHERE 

In the subsequent discussions reference is made only 
to the visible portion of the electromagnetic spectrum, 
although analogous phenomena occur with other wave 
lengths. The refractive index n\ of air for various wave 
lengths and its dependence on the air density is well 
knoAvn from laboratory determinations [31, 42]. An 
example of the magnitude of the dispersion and tem- 
perature effect on the refractive index in air at normal 
pressure (760 mm Hg) is given in Table V. Obviously, 



Table V. 


Variation of (nx-l)lO" with Wave Length 

AND TeMPEKATUHE 

{After Meggers and Peters [31]) 


X(A) 


OC 


15C 


30C 


3983 
5569 
7664 


297 
293 
290 


282 
278 
275 


268 
263 
261 



the effect of dispersion is small in comparison with that 
of temperature. The refractive indices of the various 
gaseous constituents of air differ even more significantly 
from each other, but since the composition of air varies 
only slightly, this effect is negligible for all practical 
purposes. 

Phenomena due to Average Density Gradient. When 
penetrating the atmosphere, which is assumed to con- 
sist of concentric, equidistant isopycnic surfaces, an 
extraterrestrial light ray describes a curve whose well- 
known equation is 



where r is the distance of an isopycnic surface from the 
earth's center, i the angle of incidence, and the refrac- 
tive index n (for white light) is a function of r, n(r). In 
Fig. 4, To = CO is the earth's radius; an observer at 
sees a light ray L, that enters the atmosphere at P 
with the angle of incidence i, at the apparent zenith 
distance do instead of the true zenith distance 6. The 
difference 6 — do = R, the astronomical refraction. In 
its general form, the equation of the ray curve PO in 
polar coordinates is 






or expressed in terms of astronomical refraction: 



R 



n n 
J nil 



n„ r, sin do 



i\/n-r- — nlrl sin^ 6, 



dn. 



(2) 



(3) 



The integrals, to be taken between the upper limit of the 
atmosphere (where n = nn) and the earth's surface 




nr sin i = k = const. 



(1) 



Fig. 4. — Schematic diagram of astronomical refraction. 

(index o), have no general solutions, because the change 
of n with altitude must first be known. 

Various authors made different assumptions regard- 
ing the function n(r) and computed the astronomical re- 
fraction for various apparent zenith distances. Wiinsch- 
mann [59], who compared several of the results, prefers 
Gylden's refraction data, because they are based on 
a hypothesis which agrees closely with data obtained 
from aerological ascents. Recently Link and Sekera 
[28] computed tables of various characteristics of the 
ray path for zenith distances from 75° to 90° and alti- 
tudes up to 60 km. They considered the vertical density 
distribution separately for summer and winter, using 
average density conditions as revealed by balloon 
soundings, sound propagation, and twilight phenomena. 
Correction tables for the effect of deviations from nor- 
mal in local conditions of pressure, temperature, and 
humidity have also been variously computed [31, 42]. 
These corrections are important chiefly for apparent 
zenith distances up to 70°, for which the values of R 



GENERAL METEOROLOGICAL OPTICS 



65 



are sensibly independent of the assumption regarding 
the vertical density distribution and the concentricity 
of isopycnic surfaces [28, 42, 59]. Court^ pointed out the 
inadequacy of these correction tables particularly for 
cold climates; he suggests the use, instead of air tem- 
perature, of "refractive temperature," i.e., that tem- 
perature for which the correction obtained from tables 
is the one actually required, and he presents rules for 
estimating these refractive temperatures. 

For zenith distances > 70°, Esclangon [12] attributes 
the greatest optical effect to the layer up to about 15 
km, whereas according to Wiinschmann [59] the mass 
distribution in the stratosphere between 15 and 45 km 
height and the orientation of the isopycnic surfaces in 
this layer play a dominant role. More frequent and 
systematic soundings of the upper atmosphere with 
modern equipment would enable us to solve this prob- 
lem and to obtain more direct values of stratospheric 
density variatio is. 

Wiinschmann, by means of upper-air souncHngs, con- 
structed charts showing the topography of the optical 
surfaces. He found that the influence of density varia- 
tions in the lower troposphere up to 6.5 km is generally 
compensated by an opposite influence in the upper 
tropospheric region between 6.5 and 15 km, leaving an 
insignificant net effect of the troposphere. The inclina- 
tions of isopycnic surfaces owing to local horizontal 
temperature gradients, fronts, or orographic features, 
generally change the astronomical refraction by only a 
fraction of a second of arc. 

The large astronomical refraction for zenith dis- 
tances of 90° or more generally lengthens the day, since 
it causes the sun to rise somewhat earlier and set some- 
what later than is computed from purely geometrical 
considerations. This is of practical importance for the 
prediction of illumination conditions in polar regions, 
where the strong density gradient, built up in the lower 
atmosphere during the winter night, may advance the 
date of sunrise by several days [42]. The great decrease 
in normal refraction with slight elevation above the 
horizon causes a deformation of the sun's or moon's 
disk; for the difference in refraction between the lower 
limb, touching the horizon, and the upper limb amounts 
to 6' , so that the vertical axis of the disk appears shorter 
by yi- The large refraction is connected with a rela- 
tively large prismatic dispersion which is of the order 
of 20 to 40 seconds of arc between blue and red wave 
lengths [19, 42]. This dispersion occasionally causes the 
last segment of the setting sun or planets [54] to appear 
green for a few seconds, the so-called green flash [21] 
or green segment [19]. Sometimes the color is blue or it 
changes continuously from yellow to violet. This phe- 
nomenon can occur only when the atmosphere is so 
clear that the shorter wave lengths are not attenuated. 
Whereas Hulburt [19] believes that normal dispersion 
is sufficient to cause this phenomenon, most observa- 
tions seem to be associated with refractions in excess of 
the normal [35, 54]. To what extent selective absorption 



by water vapor [42] or other gases contributes to this 
phenomenon is still undecided. 

The curvature of the rays from artificial lights is 
due to terrestrial refraction. In Fig. 5, an observer at A 
sees a point B in the direction of incidence AC of the 
curved light ray ; the angle a between the straight line 
AB and the tangent AC is the terrestrial refraction. 
Similar conditions obtain for an observer at B sighting 
point A ; in this case the terrestrial refraction is meas- 
ured by angle /3. The sum a -\- fi = e is called the total 
refraction. For an average density gradient the terres- 
trial refraction increases roughly from 2" to 42" when 
the distance between the two points increases from 1 to 
20 km [42]. The curve of the light ray can, in most cases, 
be assumed as a circular arc, so that a = /3 = e/2. The 
path of the light ray is then determined by its radius of 
curvature ri. In Fig. 5 the angular distance between 
points A and 5 is ip at the earth's center, and « is the 
central angle of the arc AB. Since the heights of A and 
B above the earth's surface are small as compared to the 




Fig. 5. — Schematic diagram of terrestrial refraction. 

earth's radius r^, and the angles e and ip are small, the 
ratio 



6 



rt 



or 



2r^' 



(4) 



As if and ?-o are known, the terrestrial refraction can be 
computed from the radius of curvature of the light 
ray. Its reciprocal, the curvature of the ray, is (ac- 
cording to Wegener [56]) determined by 



1 , ^. p 273 , , 



7), 



(5) 



3. See A. Court, "Refractive Temperature," J. Franklin 
Inst., 247:583-595 (1949). 



where Jix is the refractive index, p the barometric pres- 
sure in mm Hg, T„ the virtual temperature in °K, y 
the temperature lapse rate (counted as negative in case 
of inversions), and y' the autoconvective lapse rate. 
The curvature of the light ray is proportional to the 
barometric pressure and inversel,y proportional to the 
square of the virtual temperature, showing the dominat- 
ing influence of temperature on refraction. The curva- 
ture decreases as the lapse rate increases, and the light 
ray becomes rectilinear for a homogeneous atmosphere 
(-y = 7'). For large lapse rates, however, the con\'ective 
activity causes scintillation. For strong inversions 
(7 < < 0) the curvature of the light rays approaches 



METEOROLOGICAL OPTICS 



that of the earth's surface, which ordinarily is several 
times larger, and total reflection (mirages) may occur. 

The expansion of the horizon and the decrease of its 
angular depression is a usual consequence of terrestrial 
refraction. In Fig. 5, an observer at A whose horizontal 
plane is AH would, in case of rectilinear light rays, see 
the horizon at D, where his line of sight is tangent to 
the earth's surface and the geodetic depression is 8. 
Because of terrestrial refraction he normally sees the 
horizon at D' in the direction AD" (tangent to the 
curved ray AD'), that is, at the depression S'. The 
difference S — 5' represents the terrestrial refraction, 
and equations (4) and (5) apply to this case also. How- 
ever, 8 is generally determined by direct observation 
rather than computed from meteorological data and the 
known geometric quantities, because temperature and 
lapse rate in the air layer below the observer vary with 
the nature and contour of the underlying surface. The 
effects of these variables for air layers not in immediate 
contact with the ground were investigated by Brocks 
[2, 3, 4] who found that the terrestrial refraction can be 
quite accurately computed from meteorological data 
and that, in turn, the average lapse rate can be deter- 
mined from the observed curvature of light rays. For 
a ray -path length of 30 km, a change in zenith distance 
of 1" corresponds to a lapse-rate change of 0.04C/100 
m. By means of mutual sighting from both ends of a 
ray path the absolute values of the lapse rate can be 
determined. However, this method is of limited prac- 
tical value, because for steep lapse rates, Avith their at- 
tendant convection currents, the image fluctuations of 
the light beam would considerably decrease the accuracy 
of measurement. 

Phenomena Due to Special Density Gradients. When 
the decrease in density upwards is greater than normal, 
a condition which may be caused by smaller than nor- 
mal lapse rates, terrestrial refraction is increased and 
objects that are usually beyond the horizon come into 
view. This excessive extension of the normal horizon is 
called looming. The opposite phenomenon of sinking is 
due to an abnormally small vertical density gradient. 
As can be seen from application of equation (5) to 
the average conditions between observer and horizon 
point, the curvature l/rt of thehghtray (AD' in Fig. 5) 
becomes smaller with increase in lapse rate 7; for 
7 = 7', the curvature becomes zero and the ob- 
server sees horizon at D; for 7 > 7', his horizon would 
further shrink and end at a point between D and E, 
while the curvature becomes negative (ray convex to- 
ward surface). In this case it is not necessary that 
7 > 7' over the whole range, although this often occurs 
over strongly heated surfaces; it is sufficient that the 
isopycnic surfaces be inclined upwards toward the ob- 
server, so that the air density is greater there than at 
the distant point on the horizon [42]. The great in- 
creases in, or the reversals of, the normal vertical den- 
sity gradients are generally confined to the air layers 
near the ground. 

When the light rays from the upper portion of a 
distant object LU in Fig. 6 (A) have a different curva- 
ture than those from the lower portion, the geometric 



angle s, that the object subtends at the observer 0, 
appears changed. Exner [42] has shown that a hnear 
change in refractive index n with height cannot lead to a 
noticeable change in the angle of subtense. When the 
decrease of n with height is slower than it would be ac- 
cording to a linear function as shown by case (A), the 
curvature of the ray LO is greater than that of UO, and 
the apparent angle of subtense s' between the tangents 
to the respective rays becomes smaller. This phenom- 
enon, in which the object also appears elevated, is 
called stooping. An enlargement of s' combined with an 
apparent lifting takes place, when the decrease of n 
with height is more rapid than according to a linear 
function, as shown by case (B) which represents tower- 
ing. Whereas these phenomena result from vertical 
density gradients (drop in density per unit height) that 
decrease (A) and increase (B), respectively, with height, 
case (C) shows a negative density gradient that de- 
creases, and case (D) one that increases with height, 
causing s' to be enlarged and diminished, respectively. 







Fig. 6. — Effect of abnormal density gradients on the 
curvature of light rays. 

Because of the increase in density with height, the rays 
are convex toward the ground, and the objects appear 
depressed. The mathematical theory for these phenom- 
ena, as well as for the corresponding ones involving 
horizontal objects, was developed by Exner [42]. 

In case the density distribution in the lower layers is 
such that the rays from an object reach the observer 
along two or more different paths, so that he sees one 
or more images of the object, we speak of superior, 
inferior, or lateral mirages, depending on whether the 
image appears above, below, or to the side of the ob- 
ject. The latter case can occur only when the isopycnic 
surfaces are vertical or nearly so, for example, in prox- 
imity to strongly heated walls. This phenomenon was 
theoretically treated by Hillers [17]. In case of a com- 
plicated density distribution in the lower layers, com- 
plex distorted images of distant objects, the Fata Mor- 
gana, may appear. General theories of mirages were 
developed by Nolke, A. Wegener, and others [c. 42], and 



GENERAL METEOROLOGICAL OPTICS 



67 



more recently by Fujiwhara and others [c. 21]. There 
is, however, still a thermodynamic problem connected 
with inferior mirages such as can be observed over 
heated highway surfaces. There, the vigorous stirring 
of the air by passing vehicles apparently has little ef- 
fect on the existing density distribution. It would be 
interesting to study the "tenacity" of the mirage- 
producing air layer. Ives [24] has investigated larger- 
scale mirages of this nature and found that phenomena 
caused by steep lapse rates re-form, after disturbance, 
within a few minutes, while mirages produced by low 
inversions are more readily disturbed and "heal" much 
more slowly. Laboratory experiments, which permit 
control of the variables, and theoretical study of the 
heat transfer rate seem desirable to expand our knowl- 
edge of mirages. 

Scintillation. Scintillation is due to temporal and 
spatial variations of density in the atmosphere. It 
consists of one or more of the following characteristics, 
depending on the nature of the object viewed. If the 
object is a point source, scintillation causes (1) apparent 
directional vibrations (unsteadiness in position of fixed 
objects), (2) apparent intensity fluctuations (light 
source may even appear to flash on and off), or (3) 
color changes (white light shows alternately its in- 
dividual chromatic components). For extended objects, 
inhomogeneities in air density will cause (1) varying 
distortions of the contours or of internal line-structure 
of distant objects, thereby producing apparent expan- 
sion, contraction, or even disruption of the visible area; 
or (2) inhomogeneous brightness distribution, so-called 
shadow hands, over the surface of an object that is il- 
luminated by a coUimated light beam. 

Astronomical scintillation involves extraterrestrial 
light sources. Its effect, in general, decreases with in- 
crease in angular elevation of the source. The amplitude 
of the vibratory motion of stars (or of the edge of the 
sun's or moon's disk) amounts to a few seconds of 
arc at the most, with a frequency of roughly 2 to 30 
sec~^, although the vibrations are seldom of truly peri- 
odic nature [7, 42, 55]. The relationship between the 
quality of star images in telescopes and weather ele- 
ments has long been recognized [42] ; the image quality 
deteriorates as wind speed, turbulence, or temperature 
lapse rate in the lower atmosphere increase [2, 55]. 
Respighi [c. 42] ascribed a greater effectiveness to the 
rotation of the earth than to wind, because he observed 
spectroscopically that stars on the western horizon 
pass through the spectral color sequence from red to 
violet, while those on the eastern horizon show the 
reverse. PozdSna [43] shares this opinion, stating that 
the linear speed of the earth's rotation is much greater 
than the relative speed of the Avinds. Exner [42], how- 
ever, pointed out that the observed phenomenon was 
due to the prevailing westerlies at higher altitudes and 
suggested that the argument could be decided by means 
of observations in regions with prevailing easterly cir- 
culation. There, the phenomenon observed by Respighi 
should appear reversed if wind is the dominant factor. 
Such a test has apparently not yet been made. 

The explanation of chromatic scintillation, which 



has frequency characteristics similar to those of direc- 
tional vibrations, was given by Montigny [c. 42] and 
is briefly outlined (Fig. 7). The difference in refractive 
index for the extreme visible wave lengths causes a white 
light ray Li, entering the atmosphere at ^4, to send its 
red component toward d at the ground, its violet com- 
ponent toward an observer at 0. Another light ray 
L2, which is lower than Li by a distance D and enters 




Fig. 7. — Dispersion of light rays by the atmosphere. 

the atmosphere at B, sends its red beam toward 0, while 
its violet beam falls at O2. Other rays between Li and 
L2 send the intermediate colors toward 0, so that the 
observer there sees the entire color mixture as white, 
because the angular subtense of the spectrum is gener- 
ally too small to be resolved by the eye. The distance D 
between rays of the extreme colors varies with the 
angular elevation of the light source and the height 
above the earth's surface. Table VI represents an ab- 
stract of the corresponding table by Exner [42]. The 

Table VT. Variation op the Distance betweei^ Violet 
AND Red Rats (in cm) with Zenith Distance (O) 
AND Height (After Exner) 









Height in km 






en 














0.1 


1 


5 


10 


40 


50 








2 


3 


5 


60 


— 


— 


5 


8 


12 


70 


— 


3 


14 


22 


31 


80 


— 


15 


58 


92 


127 


84 


4 


37 


142 


224 


311 


88 


17 


151 


580 


915 


1273 


90 


50 


442 


1698 


2680 


3727 



color separation for zenith distances of < 50° is ex- 
tremely small so that chromatic scintillation of stars is 
generally not perceptible. For greater zenith distances 
and for increasing heights, the rays' separation rapidly 
increases. Any air parcel that has a density different 
from that of its environment (density schlieren) and a 
diameter less than the rays' separations, will be capable 
of diverting individual color components into a different 
direction at different instants, thus causing chromatic 
scintillation. The size of these air parcels was variously 
determined as of the order of a few centimeters to a few 
decimeters [36, 42]. The size of the schlieren in relation 
to altitude, and the schlieren velocity, obviously deter- 
mine the possibility and the frequency, respectively, of 
color fluctuations. For example, in order to produce 
chromatic scintillation of a star at 80° zenith distance, 
an air parcel must have a diameter of < 15 cm if at 1 km 
height, < 58 cm if at 5 km height, etc., whereas near 



68 



METEOROLOGICAL OPTICS 



the ground such a parcel must have an extremely small 
diameter to cause scintillation. 

The mechanism of intensity fluctuations was ex- 
plained by K. Exner [c. 42] as follows: In Fig. 8, density 
schlieren around S are embedded at certain intervals 
in an otherwise more or less homogeneous field of density 
and cause concavities (or convexities) in an originally 
plane wave-front of light and, thus, divergence of the 
rays at A and A' and convergence at B and B'. If the 
system of schlieren moves horizontally, an observer — 
say at B — will perceive alternate increases in flux dens- 
ity where the rays converge, and decreases where they 
diverge. He wifl also see the light come from slightly 
varying directions, that is, apparent vibratory motions 
of the star. It is easily envisioned that the same varia- 
tions occur if the schlieren system moves vertically. 
K. Exner measured the radius of curvature r of the 
wave-front deformation to be roughly between 2 and 
20 km. In addition to discrete schlieren, we may also 
consider the wavy structure of surfaces of temperature 
or wind discontinuity as a cause of variations in flux 
density. 



LIGHT RAYS 




Fig. 8. — Scintillation resulting from density schlieren 
{after K. Exner). 

The short-term fluctuations of images received from 
terrestrial light sources or objects, or terrestrial scin- 
tillation, is of great practical importance; in particular, 
strong scintillation may interfere with blinker signaling. 
Scintillation also limits the precision of telescope point- 
ing and the useful magnification of telescopic devices 
[46]. Siedentopf and Wisshak'' recently investigated the 
case of collimated light sources over a range 1 km long 
and 1 m above the ground, employing an objective 
receiver. With strong scintillation, the frequency of 
apparent intensity fluctuations was most often observed 
between 5 and 9 sec~^ with lesser scintillation between 
1 and 3 sec^^ The whole range covered the frequencies 
between 1 and 50 sec~^ The relative variability of the 
apparent intensity ranged between and 100 per cent 
and did not materially increase with lengthening of the 
ray path* beyond 1 km. The mean frequency of intens- 
ity fluctuation was found to be independent of the path 
length. Shadow bands of from 5 to 10 cm width and 
several seconds duration were also observed moving 
horizontally with the wind across a screen several 
hundred meters from the searchlight. 

The fact that an air column of 1 km length produces 
almost the entire effect of scintillation shows that the 



4. R. Meyer [36] cites their paper as unpublished and gives 
a concise summary of their results. 

5. According to K. Exner's results, the minimum source 
distance that chromatic terrestrial scintillation is observable 
is about 10 km [c. 42]. 



density discontinuities near the receiver are optically 
the most effective. Brocks [2] similarly found that the 
atmospheric conditions in the first tenth of a horizontal 
ray path (counting from the observer) are nineteen 
times as effectual in producing scintillation as the same 
conditions in the last tenth of the path. This seems to 
be the reason why various meteorological elements, 
observed near the receiver, correlate so well with the 
degree of terrestrial (and to a certain extent, astronomi- 
cal) scintillation that predictions of atmospheric optical 
conditions are possible [4, 24, 42, 55]. Such predictions 
may not hold where, for example, thermal turbulence 
is present near the light source but not near the receiver. 
In this case, scintillation presumably could still occur, 
if, at the receiver, the angular subtense of the responsible 
air parcels were large as compared to that of the light 
source. Also, in cases in which the central portion of very 
long rays grazes the earth's surface, this portion is 
particularly exposed to density discontinuities that may 
not exist at the elevated end points of the rays. 

The optical distortions by the atmosphere of non- 
luminescent, diffusely reflecting sources are generally 
referred to as shimmer, or atmospheric hoil. Riggs and 
others [46] measured photographically the apparent 
lateral displacement of vertical linear targets and the 
distortion of rectangular grids at several hundred meters 
distance. They found angular deviations from the mean 
position of line elements of the order of 1" to 5". For 
targets separated by more than 3' to 5', there was no 
appreciable coherence of the observed deviations, that 
is, the horizontal dimensions of the schlieren subtended, 
at the camera, angles of less than 3' to 5'. Unfortunately, 
no exact linear dimensions of the experimental arrange- 
ment are given, so that only the minimum size of the 
air parcels can be estimated (roughly 10 cm). In general, 
the characteristics of terrestrial scintillation appear to 
be very similar to those of astronomical scintillation; 
this fact indicates that the cause of the latter must lie 
predominantly in the lower layers of the atmosphere. 
Nevertheless, the extent to which the upper atmosphere 
contributes to astronomical scintillation must still be 
considered an open question, whose answer must come 
from direct exploration of the properties of the upper 
air. 

The theories of scintillation by Montigny, K. Exner, 
and others [c. 42] explain qualitatively the observed 
phenomena. However, an exact mathematical expres- 
sion of the relationship between the frequency and 
amplitude of apparent object motion, apparent intensity 
fluctuations, and chromatic effects on the one hand, and 
periodic time-space variations of meteorological factors 
on the other, remains undeveloped. There are also 
experimental problems as follows: The scintillatory be- 
havior of uncollimated and difi^use light sources needs 
further investigation, although it is to be expected that 
diffuse sources will show a much lesser degree of scintil- J 
lation than do collimated sources. Of particular interest ' 
would be an investigation into the size, shape, spacing, 
and transport velocity of schlieren in relation to the 
size, distance, and optical characteristics of the light 
source for various degrees of scintillation. Such studies 



GENERAL METEOROLOGICAL OPTICS 



69 



could be made, for example, with the aid of a spatial 
arrangement of a field of light sources and receivers in 
connection with a dense micrometeorological network. 
For recording the apparent vibration of objects, motion 
picture cameras could be employed, whereas photo- 
electric devices seem to be preferable for measuring the 
apparent intensity fluctuations. The variation of scintil- 
lation with the altitude of the ray path above the 
ground, as well as with oblique upward and downward 
direction of the rays, is another problem which seems 
of practical interest for flight operations. 

PHENOMENA DUE TO ATMOSPHERIC 
SUSPENSIONS 

In this section, the sun is considered as the source of 
light, although the moon or artificial luminants may 
also produce the phenomena. 

Hales. The term "halo," although implying ring 
shape, is generally applied to all optical phenomena 
that are produced by ice crystals suspended in the 
atmosphere and, occasionally, by those deposited on 
the ground [34, 36]. 

In Fig. 9, the sun is roughly 25° above the horizon 
HH; ring A represents the 2^ -halo (radius 22°), ring B 
the 46°-halo. The two parhelia CC lie to the right and 
left of the sun at the same elevation, but at angular 
distances from the sun that vary between 22° and 32° 
for sun's elevations between 0° and 50°, respectively. 
The parhelic circle DD through the sun and parallel to 
the horizon is rarely seen as a complete ring; often only 
short segments of it extend outward from the parhelia. 
Tangent to the 22°-halo are the upper and lower tangent 
arcs EE and E'E', respectively, which are only one of 
the metamorphic forms of the circumscribed halo. This 
halo is truly circumscribed only for sun's elevation of 
> 30°. For the various forms of this halo see pertinent 
literature [21, 34, 42]. The lateral tangent arcs of the 
22°-halo, or Lowitz-arcs, FF, curve concavely toward 
the sun from the parhelia and touch the 22°-halo below 
its equator. The vertex (in the sun's meridian) of the 
Parry-arc G has an angular distance from the sun that 
decreases from 43° at 0° sun's elevation to tangency 
with the 22°-halo for sun's elevations between 40° and 
60°, and then increases again for higher sun's elevations. 
The circumzenithal arc J is centered around the zenith 
and very near, or even tangent to, the 46°-halo. The 
infralateral tangent arcs of the 46°-halo are repi'esented 
by KK; these arcs also are metamorphosed as their 
points of tangency move downward and meet at a sun's 
elevation of 68°, while at the same time their curvature 
(convex toward the sun) decreases and reverses itself 
for sun's elevations > 58°. The single arc separates from 
the 46°-halo when the sun is higher than 68°. The 
sun pillar LL lies in the sun's meridian and is, like the 
parhelic circle, generally white because of its origin 
by reflection, whereas the other halos are produced by 
refraction and thus more or less colored. 

There are also other halos, such as the circiimhori- 
zontal arc that corresponds to the circumzenithal are, 
but lies about 46° below the sun. Supralateral tangent 
arcs of the 46° -halo correspond to the infi'alateral arcs. 



On the sky opposite the sun, the anthelion, a bright spot 
on the parhelic circle, is sometimes obliquely crossed by 
anihelic arcs. Also rings of unusual radii, 8-9°, 17-19°, 
23-24°, etc., have been observed on rare occasions, as 
well as skewed forms such as inclined pillars and par- 
helic circles, and secondary phenomena caused by reflec- 
tion or refraction of light emitted from primary halos. 
The geometrical optics of the various halo phenomena 
was theoretically treated by various authors [21, 34, 
42, 44, 58]. In general, most phenomena can be ex- 
plained by refraction with minimum deflection and/or 
by reflection involving simple hexagonal ice crystals of 
columnar or platelet shape, ■with various attitudes and, 
in some cases, oscillating motion while falling. The 
principal genetic features of the major halo phenomena 
are summarized in Table VII, in which the optical 
relationship, for example, between the circumzenithal 
arc and the infralateral arcs of the 46°-halo, becomes 
evident. There are, however, many phenomena that 
have been explained by different patterns of ray paths, 
or by more complicated crystals or crystal aggregates. 
Thus, for example, the optical origin of the anthelion, 
its oblique arcs [53], Hevelius' parhelia at about 90° 




Fig. 9. — Schematic view of major halo phenomena. 

from the sun, and other phenomena, is still uncertain; 
Bouguer's halo, a white ring of about 38° radius around 
the anthelic point, may even be a fogbow produced by 
very small supercooled water droplets [34, 47]. Decisive 
explanations will not come from additional theories, 
but from an accumulation of better observations. In 
particular, sampling of the ice crystals producing rare 
halos or those of lurcertain origin would be most desir- 
able. Many halos, theoretically established, have never 
been observed [58] ; on the other hand, some phenomena, 
such as those observed by Arctowski [c. 42], are still 
unexplained. Meyer [34] discusses the various geometric 
problems of halo phenomena, and outlines as prerequi- 
sites for a complete theory the various physical aspects, 
such as the concentration of ice crystals in the clouds, 
and the brightness and polarization of the halos relative 
to those of the clouds in the environment. The physical 
optics of halos is almost entirely unexplored ; in addition 
to refraction and/or reflection by ice crystals, diffrac- 
tion plays a role in the formation of halos [34, 42]. 
Photometric observations, that have been introduced 
into halo investigations by E. and D. Briiche [5], would 
advance our pertinent knowledge of halos and the 
constitution of ice clouds [34]. 



70 



METEOROLOGICAL OPTICS 



The frequency of different halos, their diurnal and 
annual or seasonal variations, and their relation to 
weather situations, have been investigated [1, c. 34, 52]. 
The similarities or differences in the results can generally 
be ascribed to climatic characteristics. The relationship 
between halo occurrence and solar activity is, however, 
still quite problematic. Visser [52] found a decrease in 
halo frequency with increasing relative number of sun- 
spots* up to 90 and then an increase for higher sunspot 
numbers. Archenhold [1] arrived at a direct linear 
relationship, and a halo periodicity of 27-28 days, which 
he associates with the rotation of the sun. This periodic- 



rainbow, whose radius to the red inner border is about 
51°. Inside the primary and outside the secondary bow, 
suTpernumerary bows showing fewer and fainter colors 
are often visible. When the sun's rays are reflected by a 
smooth water surface ' before striking the suspended 
droplets, primary and secondary reflection rainbows may 
appear whose center lies as much above the horizon as 
that of the regular bows lies below it. Thus, the reflec- 
tion bows intersect the respective regular ones at the 
horizon. When the reflecting water surface is undulated 
by a smooth swell, the reflection bow may deform into 
vertical shafts [57]. Droplets of radii < 30 m may pro- 



Table VII. Principal Genetic 


Features op 


Major Halo Phenomena 


Halo 


Refracting angle 


Orientation of 

principal crystal 

axis 


Special characteristics (s = sun's elevation) 


22° 


60° 


Random 


Incident ray at 90° to principal axis. 


Parhelia 


60° 


Vertical 


Intensity rapidly decreases for s > 50°. 


Circumscribed to 22°-halo 


60° 


Horizontal 


Upper and lower tangent arcs join at s fe 30°. 
At s 6 55° elliptic with long horizontal axis. 
At s = 90° circular and coincides with 22°-halo. 


Parry -arcs 


60° 


Horizontal 


Pair of crystal sides vertical for s < 30°, horizontal 
for 30° < s < 50°. 


46° 


90° 


Random 


Incident ray at 90° to principal axis. 


Circumzenithal arc 


90° 


Vertical 


Ray entrance at crystal base; limited to s g 32°; 
also possible with horizontal axis and pair of 
sides horizontal, but rare. 


Cricumhorizontal arc 


90° 


Vertical 


Ray entrance at crystal side; limited to s § 58°; 
also possible with horizontal axis and pair of 
sides horizontal. 


Lateral tangent arcs of 22°-haIo (Lowitz- 
arcs) 


60° 


Oscillating 


Oscillation < ±30° about verticail in plane that is 
parallel to sun's meridional plane. Limited to 
25° < s < 55°. 


Infralateral tangent arcs of 46°-halo 


90° 


Horizontal 


Ray entrance at crystal base. Limited to 0° < s 
< 68°. 


Supralateral tangent arcs of 46°-halo 


90° 


Horizontal 


Ray entrance at crystal side. Limited to 0° < s 
< 32°. 



ity was shown to be spurious [39]. Although a certain 
degree of correlation with solar activity seems to exist, 
there is hardly a direct relationship {e.g., corpuscular 
solar radiation furnishing sublimation nuclei), consider- 
ing the prerequisites that must be fulfilled for a halo to 
be observable [34, 39]. 

Rainbows. The colorful arcs around the antisolar 
point that appear on sheets of water droplets are called 
rainbows, although these phenomena may be produced 
by dew droplets on the ground or water sprays. The 
primary rainbow has an angular radius to the red outer 
border of roughly 42°; concentric to it is the secondary 

6. According to Schindler [c. 36], a relationship between 
sunspots and halos begins only at a spot number of 35 to 40. 



duce a broad white band with faintly tinted borders, 
the fogbow, between about 37° and 40° distance from 
the antisolar point. Rainbows or fogbows produced by 
drops in a horizontal plane appear in the form of conic 
sections, that is, hyperbolic, elliptic, or parabolic arcs, 
depending on whether the sun's elevation is respectively 
smaller than, larger than, or equal to, the aperture of the 
cone (42° or 51°). 

The well-known explanation by Descartes considered 
geometrical optics alone. Airy, basing his theory on 
wave optics, explained the variation of colors with 
droplet size and the supernumeraries as interference 
rings. His rainbow integral was also solved by others. 
The distribution of intensity, color, and polarization of 



GENERAL METEOROLOGICAL OPTICS 



71 



the light after refraction and reflection by the droplets 
was computed, notably by Pernter and Mobius [c. 42]. 
Bucerius [6] developed an asj'mptotic method (in anal- 
ogy to Debye's treatment of cylindric functions) by 
means of which Mie's theory of scattering of electromag- 
netic waves by dielectric spheres [c. 29] can be extended 
to large waterdrops. Applying this general theory to the 
rainbow phenomenon, he showed that it contains the 
older rainbow theories as approximations, and that the 
rainbow is an areal phenomenon that actually covers 
the entire region between the antisolar point and the 
first ring. Meyer [36] considers the classical diffraction 
theory still adequate, particularly for the intense rain- 
bows that originate from comparatively large droplets. 
He developed this theory further to permit the deter- 
mination of the luminous density of rainbows. He takes 
into consideration the total optical effect of all droplets 
contained in a surface element of the cloud deck, the 
thickness of the cloud, and the attenuation of the rays 
to and from the cloud. He finds the luminous density 
of the primary rainbow to be twelve times that of the 
secondary bow. 

The theoretical advancement of our knowledge of 
rainbows appears to have surpassed our fund of observa- 
tional data. Aside from older visual measurements, there 
are, to my knowledge, no results of up-to-date colori- 
metric photometry of rainbows available for application 
to the theoretical findings. In this connection an almost 
forgotten problem may be recalled, the fluctuations of 
colors during lightning and thunder [42], an observation 
requiring objective verification and explanation. 

Corona and Related Phenomena. The sun shining 
through relatively thin clouds often produces one or 
more sets of colored rings, the corona, having diameters 
of a few degrees. When poorly developed, only an aureole, 
a bluish -white disk with brownish rim, may be visible. 
After violent volcanic eruptions, a broad reddish-brown 
ring of large radius (20° and more), Bishop's ring, has 
been observed in dust clouds [11]. We speak of iridescent 
clouds, when the colors are not arranged concentrically 
around the sun, but are irregularly distributed over, or 
follow the contours of, the cloud. This group of coronal 
phenomena around the sun is paralleled around the 
antisolar point by a similar group: An observer, seeing 
his slightly enlarged shadow, the Bracken-specter, on 
a fog bank or cloud, often finds the shadow of his head 
surrounded by one or more sets of colored rings, the 
anticorona or glory, well-known to pilots. If the shadow 
falls on a bedewed surface on the ground at some dis- 
tance from the observer, the shadow of his head may be 
rinmied by a narrow white sheen, the heiligenschein, 
which also can be observed around one's head-shadow 
on a beaded projection screen. 

The classical diffraction theory applied to the corona, 
under the assumption that the droplets are opaque, has 
been found to be in fair agreement \vith observations 
[42]. The well-known approximation formula by K. 
Exner [c. 42] for the angular radius d of the circulai' 
intensity minima produced by particles of the diameter 
d in light of wave length X, is 

sin e = {N + a)X/d, (6) 



where A'' is the order of the minimum counting from the 
center, a = 0.22 for spherical, a = for nonspherical 
particles. Ramachandran [45] based his new corona 
theory on wave optics and included the wave-front 
portion that is transmitted through the droplets. In 
Fig. 10 the results of his calculation of intensities 
(X = 0.5 ju) at various diffraction angles (6) for small 
droplets (radii in m ascribed to the curves) are repro- 
duced. These curves indicate that the ring systems 
oscillate as the small droplets increase in size. Only 
relatively large droplets diffract like opaque disks of 
the same size, which explains some of the discrepancies 
formerly noted between the classical theory and 
observations. The position of the ring systems appears 



40 




Fig. 10. — Intensity of diffracted light as funetion of angular 
distance from light source. {After Ramachandran. Ordinate 
scale presumably in relative units; numbers on curves are 
drop radii in microns.) 

unaffected by the thickness and density of the clouds. 
Bucerius' work [6], mentioned above, also includes the 
application of the rigorous diffraction theory by Mie 
[c. 29] to both corona and anticorona. The anticorona 
was similarly treated by van de Hulst [20]. This theory 
yields the intensity and polarization of the diffracted 
light and the position of intensity maxima and minima. 
Table VIII gives a comparison of the values for the 
argument of the Bessel function at which corona 
maxima occur according to the old and the newer 
theories. It is noteworthy that in Ramachandran'3 
theory the location and intensity of the maximum for 
small drops also depends on the value of (sin ^)/?, where 
5 is a function of rf/X. For this reason the maxima 
oscillate as shown in Fig. 10. According to Bucerius 
[6, equation (47)], the argument contains tmce the sine 
of half the angle between primary and diffracted rays, 



72 



METEOROLOGICAL OPTICS 



instead of the sine of the whole angle d. This is also true 
for the anticorona [6, equation (48)], the theory of which 
shows that it is produced by rearward diffraction, not 
by reflection of the primary ray with subsequent for- 
ward diffraction [Richarz, c. 42]. Bucerius' results may 
be summarized as follows: The intensity of the corona 
is a;2 = (ird/X)- times as great as that of the anticorona; 
the intensity at the center of the anticorona is a mini- 
mum, that of the corona a maximum. Values for the 
angle 6 of the successive intensity maxima of the anti- 
corona^ are determined by 2x sin (6/2) = 3.05, 6.7, 
10.0, 13.2, • • • ; the minima are located at relatively 
the same position as are the corona maxima (Table 
VIII). This explains why the application of the classical 
corona formula (6) to the minima of the anticorona 
yielded values of the drop diameter d, that varied with 
the order of the minimum [c. 42, 47]. Also the decrease 
in intensity of successive maxima is much greater for 
the corona than for the anticorona; therefoi'e, multiple 
glories are more frequently observable than multiple 
coronas. 

The old controversy regarding the possibility of cor- 
onas and glories in ice-crystal clouds [21] now stands as 



Unfortunately, none of the new theories considers dif- 
fraction by nonspherical particles, so that no final 
decision can be made. 

Iridescence of clouds is explained as diffraction pat- 
terns produced by groups of uniform droplets that vary 
in size in different portions of the cloud. In view of the 
great sensitivity of the diffraction patterns to slight 
differences in size of small droplets [45] (Fig. 10), it is no 
longer difficult to explain the occurrence of iridescence 
at relatively large angular distances from the sun [c. 42]. 
The heiligenschein is considered the result of external 
reflection by the dew droplets [21, 42]; to what extent 
diffraction plays a role in this phenomenon is not 
known. Experimental data or intensity measurements 
are completely lacking. 

The corona and anticorona have been widely em- 
ployed in the study of cloud and fog elements. Measure- 
ments were largely confined to the angular radius of 
prominent rings and subsequent evaluation in terms of 
droplet radius. In view of recent theoretical develop- 
ments [6, 20, 45] this geometric method seems unre- 
liable; also the difficulty in visually locating diffuse 
rings, produced by inhomogeneous fogs or clouds, causes 



Table VIII. Comparison of Position of Corona Maxima of Various Orders According to Different Theories 





Argument of Bessel Function 


Order of Maximum 




1 


2 


3 


4 


5 


Masoart [c. 21] 
Ramachandran [45] 
Bucerius [6] 


> T d(sin e)/\ 
2,r d(sin e/2)/\ 


5.14 

5.14 
5.1 


8.46 
8.42 
8.4 


11.67 
11.62 
11.6 


14.84 
14.78 
14.8 


17.98 
17.96 



follows: Multiple-colored rings generally indicate the 
presence of water droplets; however, the production of 
faintly colored glories by ice clouds has been established 
[47]. A statistical survey by Peppier [41] revealed that 
78 per cent of glories were simultaneously obsei'ved with 
fogbows at temperatures between OC and — 4C; a 
maximum frequency of glories occurs at about — 4C, 
that of halos at about — 12C. Nevertheless, the fre- 
quency curves of anticoronas and halos overlap in a 
wide range of temperatures from about — 2C to < 
— 20C. At any rate, this problem cannot be considered 
solved. Statistical analyses of the occurrence of diffrac- 
tion rings simultaneously with halos or fogbows reveal, 
at best, the relative frequency of diffraction rings in ice 
and water clouds, respectively, but are entirely incon- 
clusive regarding the physical possibility of these phe- 
nomena in ice clouds. Moreover, Stranz [c. 36] by means 
of photronic cells, detected multiple coronas that were 
invisible to the eye. The theoretical objections to the 
possibility of diffraction phenomena produced by ice 
clouds were mainly based on the optical properties and 
orientation of ice needles, but other possible crystal 
forms must also be considered. Moreover, the occurrence 
of Bishop's ring in dust clouds shows that nonspherical 
particles are capable of producing diffraction rings. 

7. Bucerius (also [36]) gives here 27ri- sin (6/2), but refers 
to it as the argument of the Bessel function which, however, 
appears as 27rd(sin 8/2)/\ = 2x sin (6/2). 



considerable uncertainties (see [5]). In the future it 
would be preferable to resort to objective monochro- 
matic photometry of the entire zone around the light 
source (or shadow center), and perhaps, to determine 
the intensity of the diffracted light separately for the, 
two components of polarization. Simultaneous deter- 
mination of the droplet size by other means could serve 
as a check of the theory by making possible a compari- 
son between observed and theoretical intensity dis- 
tributions, rather than a comparison of only the minima 
or maxima. 

Considering the rarity of homogeneous fogs, a theo- 
retical and experimental study of inhomogeneous fogs 
appears of particular practical importance. Also, a final 
answer to the question of the possibility of coronas in 
ice clouds would give the observer on the ground a tool 
for the identification of the physical state of the clouds. 

TWILIGHT PHENOMENA 

The investigation of twilight phenomena is closely 
connected with the study of the optical properties of 
the upper atmosphere, at least to a height of 60 km 
[18] and, thus, indirectly with the study of its density 
and dust content. The discussion of the temporal de- 
velopments of the various phenomena is based on the 
sunset and the sun's meridian. Figure 11 shows the 
nomenclature for the significant astronomic-geometric 
features pertaining to the half -space above the observer 
and a schematic view of the major phenomena. 



GENERAL METEOROLOGICAL OPTICS 



73 



Description. At, or shortly after, sunset, the anti- 
twilight arch, a purphsh band of some 3° or more in 
■width, can be seen to rise above the solar counterpoint 
on the eastern horizon. At about 1° sun's depression, 
the gray-blue dark segment or earth's shadow begins to 
rise beneath the antitwilight arch. At approximately 2° 
sun's depression, the purple light appears as a purplish 
area above the solar point in the western sky. This area 
has a vertical angular extent of 10° to 50°, a lateral ex- 
tent of 40° to 80°. Its upper boundary, which has an 
elevation of about 50° at the beginning, descends stead- 
ily to the horizon. The purple light reaches its maxi- 
mum intensity at about 4° sun's depression and usually 
disappears at about 6° sun's depression. The rising anti- 
twilight arch usually fades from view when the purple 
light is at its height, and shortly afterwards, the dark 
segment becomes indistinguishable from the rest of the 
darkening sky. Its transit through the zenith generally 
cannot be observed, but it reappears as the bright seg- 
ment^ or twilight arch above the solar point, when the 
sun's depression is about 7°. The bright segment disap- 
pears below the western horizon at about 16° sun's 
depression. 



ZENITH 



PURPLE LIGHT 




HORIZON 



SOLAR POINT 
SLIM 



Fig. 11. — Schematic diagram of major twilight phenomena 
(elevation angles are a = antitwilight arch, /3 = maximum 
purple light intensity, 7 and 7' = upper and lower boundary 
of purple light, b = antisolar point, and e = dark segment). 

When the sun's rays are partially obstructed by 
clouds or mountain peaks, the purple light may assume 
a ray-structure because of the interruption by the sha- 
dow bands (crepuscular rays) which seem to converge 
towards the sun. Similarly, the continuation of these 
shadow bands (anticrepuscular rays) on the eastern sky 
may give the antitwilight arch a fanlike appearance. 
Colored illustrations of the various twilight phenomena 
can be found in [16]. 

During brilliant twilight phenomena, a secondaiy 
purple light may become visible after the main piu'ple 
light has disappeared. Also a secondary antitwilight 
arch and dark segment may develop within the primary 
dark segment. These secondary phenomena are much 
more diffuse in outline and show fainter colors. 



S. The descriptive term "bright segment" is preferable 
because of its fundamental identity with the dark segment and 
the basic difference from the "antitwilight arch." The term 
"earth's shadow" is physicallj' incorrect [40] and does not 
readily permit differentiation between the phenomena on 
either side of the zenith. 



For the measurements of twilight phenomena the 
following spatial and temporal aspects are generally 
considered: The elevation angle of the upper boundary 
of the antitwilight arch, of dark and bright segments, 
and of purple light; and the sun's depression at the 
time of beginning, end, and maximum intensity of the 
purple light. In addition, photometric measurements of 
the light intensity in various spectral ranges along sig- 
nificant portions of the sun's meridian are of major 
interest. 

Results of Observations. The development pattern 
of the purple light has been found to be practically 
the same everywhere except at altitudes above 2000 
m where the pui'ple light ends at somewhat greater sun's 
depressions and where its upper boundary reaches 
greater elevations. A greatly detailed analysis of visual 
observations, such as made by Gruner [14] and Dorno 
[11], seems hardly warranted in view of the fact that 
the sun's depressions are computed without regard to 
the variable refraction, that the intensity is estimated 
according to a memory scale, and that the measurement 
of elevation of the diffuse boundary of the delicately 
tinted phenomenon is affected by subjective factors 
[50]. In Europe, a maximum frequency of bright purple 
hghts occurs in autumn, a minimum in spring; this 
fact has been attributed to the corresponding frequency 
of anticyclones with clear skies in that area [51]. Other- 
wise no significant relationship between weather and 
purple hghts has been found. 

Secular variations of intense purple lights have been 
observed associated with dust produced by volcanic 
eruptions [c. 42, 50]. There exists, however, a time lag; 
for example, after the Katmai eruption in summer 1912, 
purple lights did not reach their maximum intensity 
until summer 1913 [11]; this delay was obviously due 
to the time involved in the sedimentation of dust parti- 
cles necessary to produce the optimum concentration 
and size distribution for the formation of the purple 
light. For this reason, an absence of dust layers cannot 
be deduced from an absence of intense purple lights 
[50]. 

Although visual observations have long been recog- 
nized as inadequate, objective methods have been em- 
ployed only in relatively recent times [13, 14, 32]. The 
techniques involved still need improvement and stand- 
ardization. The results obtained at different stations 
from photoelectric [13] and photographic [32] intensity- 
measurements with color filters show a maximum red 
content of the sky light between 4° and 5° sun's depres- 
sion, corresponding to the visually observed maximum 
relative intensity of the purple light. The absolute 
luminous density of the sky light decreases steadily in 
all spectral ranges with increasing sun's depression in 
contrast to the visual impression [14]. ^Vhereas the re- 
sults from visual observations were essentially con- 
firmed by objective methods [13], the latter have shown 
the presence of the purple light when the spectral dif- 
ferences in intensity were below the threshold of visual 
perception [32]. 

Gruner [14] has indicated a method for determining 



74 



METEOROLOGICAL OPTICS 



the height of the layer responsible for the purple light. 
By graphical approximation he arrived at values be- 
tween 25 and 31 Ian for the upper boundary of the 
layer, and 18 km for the thickness of the generating ray 
beam, that is, a thickness of the layer of roughly the 
same magnitude. Smosarski [c. 14, 50] estimated the 
lower boundary at 8 km and the upper boundary at 
17 km. The relationship between purple lights and 
high dust layers of volcanic origin seems to confirm at 
least the order of magnitude of these values. The pos- 
sibility of a connection with the ozone layer is an un- 
explored question. Incidentally, Gruner [14], assuming 
the purple light to be a corona, also determined the 
order of magnitude of the particle diameter as between 
1 and 1.5 m- For these small particles, however, the 
classical diffraction theory fails [45] as was shown in the 
preceding section. 




POINT - 



Fig. 12.- 



4 5 6 7 8 9 10 II 12 13 14 15 
SUN'S DEPRESSION (") 

-Average course of dark and bright segments at two 
Swiss stations. 



Several series of geometric measurements of the ele- 
vation of the upper boundary and the width of the anti- 
twilight arch have been made. The course of its angular 
elevation is similar to that of the dark segment (Fig. 
12). Mendelssohn and Dember [33] made a few spectral 
measurements by photographic photometry, but their re- 
sults confuse, rather than elucidate, the visual observa- 
tion. The armual and secular variations of antitwilight- 
arch occurrence were determined by Smosarski [SO] who 
found, in Poland, a maximum frequency in autumn and 
winter, a minimum in summer, and a good correlation 
with volcanic activities. A direct connection with the 
occurrence of purple lights does not seem to exist. Ac- 
cording to computations by Smosarski [c. 14], as the 
sun's depression increases, the antitwilight arch is pro- 
duced by the rearward scattering of sunlight by smaller 
particles at higher altitudes. However, according to 
Mendelssohn and Dember [33], the antitmlight arch 
is supposedly fixed in a layer between 4 and 9 km. This 
problem will be discussed below. 



Of the many observations on the movement of the 
dark and bright segments, only the averages of two 
series obtained at Piz Languard (3280 m) and Steck- 
born (430 m) in Switzerland, as reported by Gruner 
[14], are sho'WTi as examples in Fig. 12. As the sun sinks 
below the horizon, the dark segment rises more rapidly 
than does the antisolar point; the ascent rate increases 
with the sun's depression, until the segment fades from 
view between 5° and 6° depression. Between 7° and 8° 
depression the bright segment appears at an elevation of 
roughly 25° above the solar point and descends, first 
rapidly then more slowly, to the western horizon. Ac- 
cording to the interpolated (dashed) portions of the 
curves, the invisible transit through the zenith occurs 
at a sun's depression between 6° and 7°. This agrees 
well with observations of the zenith brightness by 
Brunner [c. 14] and Hulburt [18], and of global illumi- 
nation by Siedentopf and Holl [48]; these authors pre- 
sent curves of brightness and illumination, respectively, 
versus sun's depression, that show a definite inflection 
point between 6° and 7° sun's depressions. This fact is 
involved in the problem of the height at which this 
phenomenon occurs. In this connection the change in 
relative variability of the dark segment's elevation at 
various sun's depressions deserves attention. It has 
been shown [26, 40] that the variability decreases rap- 
idly until the sun's depression is about 2.5°, then more 
slowly, although the opposite trend was to be expected 
in view of the decreased accuracy of measurement at 
greater sun's depressions. This fact was interpreted as 
being caused by a transition of the dark segment at 
about 2.5° sun's depression into the stratosphere, where 
marked changes in turbidity from day to day are less 
frequent [40]. 

The sun's depressions at which the last traces of the 
bright segment disappear below the' horizon have been 
variously used to compute the height at which the 
density of the atmosphere is sufficiently great to produce 
visible scattering of the direct sunlight. However, the 
resulting values of 50-65 km [14] are still quite prob- 
lematic because of subjective factors involved in the 
perception of faint light and of the effects of attenua- 
tion of the direct light rays at various altitudes. Ex- 
cept for a slight increase in elevation of the dark seg- 
ment in summer and with diminished transparency of 
the lower layers of the atmosphere, no clear-cut rela- 
tionships between the turbidity of the air and the 
bright segment, nor a definite seasonal variation of 
either segment have been established [14, 16, 18, 26, 
40]. 

Theories and Problems. Although many theoretical 
approaches to the problems of twilight phenomena 
have been made, no complete theory exists as yet. The 
theories of the dark and bright segments and of the 
antitwilight arch [15, 16] agree qualitatively with, but 
differ quantitatively from, the observations. For exam- 
ple, the elevations of the dark segment, computed from 
the spectral intensities of light scattered by a Rayleigh 
atmosphere (disregarding multiple scattering), were 
considerably smaller than the observed ones [14, 15]. 
The principal ideas underlying the explanations of 



GENERAL METEOROLOGICAL OPTICS 



75 



the segments and antitwilight arch are schematically 
demonstrated with the aid of Fig. 13 as follows: Ro to 
Rs are sun's rays passing through the atmosphere whose 
optically effective height may be E3D3. The lowest ray 
Ro touches the earth's surface at Og. Owing to scatter- 
ing and absorption on their way through the air, any 
rays between Ro and Ri lose part of their short-wave 
components and their intensity is depleted, so that Ro 
may not reach much beyond Oo, the next higher ray a 
little farther, and so on. The envelope of the end points 
of all these rays is represented by the curve OoDiD^Ds. 
Consequently, the atmosphere to the right of this curve 
lies in the shadow of the earth. An observer Oi, for 
whom the sun's depression is 5i, sights the vertex of the 
dark segment at Di, the point of tangency of his line 
of sight OySi to the ray envelope. If he raises his line of 
sight slightly, he perceives light scattered from the still 
illuminated portion of the atmosphere near the enve- 
lope. This prevalently reddish hght constitutes the anti- 
twilight arch. Its upper boundary is seen when the line 
of sight at Oi is further raised so that the diminishing 
light from the zone of red rays is compensated by the 
increasing light of shorter wave lengths from the higher 




Fig. 13. — Schematic diagram for the dark and bright segments. 

layers of the atmosphere. When the sun sinks further, 
the relative position of the observer shifts to O2, where 
the line of sight 02<S2 touches the envelope at D2. For 
an observer at £'3, the passage of the dark segment 
through the zenith is imperceptible, because there is 
not enough contrast between the sky brightness to the 
right and left of the line of sight EzD^. Finally, the ob- 
server at O3 sees the bright segment at an elevation e. 
The geometric aspects of this problem have been 
studied by various authors [c. 14, 40]. The results of 
computations of the heights of points D at various 
sun's depressions, although based on different assump- 
tions, agree fairly well as shown by the examples in 
Table IX. According to these heights, point D moves 
into the stratosphere at a sun's depression between 2° 
and 3°, in agreement with the deductions made from 
the variability of the dark segment. However, the prob- 
lem is essentially a photometric one [42]. An attempt at 
a physical solution was made by Dember and Uibe 
[10], who took into consideration the visibility as pro- 
portional to the square root of the measured sky bright- 
ness. Application of this theory by Mendelssohn [33] 
to photometric measurement yielded a constant height 
of the dark segment between 2 and 4 km. However, the 
transit of the dark segment would then have to occur 
not later than at about 3.5° sun's depression [40], which 



is contrary to observation. Nevertheless, the basic idea 
of including the attenuation of light along the line of 
sight is correct. This was suggested by Exner [42] who, 
however, based his formula on Rayleigh scattering alone 
and disregarded secondary scattering which undoubt- 
edly plays a role in the brightness of the sky below the 
ray envelope [18]. 

Table IX. Height of Dark Segment at Varioits 
Sun's Depressions 



SO 


Mohn [c. 14] (km) 


Neuberger [40] (Ion) 


1 





2 


2 


11 


8 


3 


21 


17 


4 


31 


27 


5 


40 


38 



The major problematic factors pertaining to the seg- 
ments and antitwilight arch are as follows: Two in- 
fluences on the ray envelope must be considered, that 
of atmospheric refraction which causes a vertical di- 
vergence of the sun's rays (shown as parallels in Fig. 
13), and that of atmospheric attenuation of the rays 
near the ground. This attenuation tends to counteract 
the effect of refraction by ehminating the lowest, most 
refracted rays [27]. The position and shape of the ray 
envelope is, thus, primarily a function of the trans- 
parency of the atmosphere at and above the point of 
tangency with the earth's surface. As regards the in- 
tensity and color of the scattered light, most computa- 
tions have been based on an idealized atmosphere in 
which Rayleigh's theory with its synunetric scattering 
function is valid [14, 15, 18]. However, the real atmos- 
phere contains a large number of particles, especially 
in the lower layers. For this reason, the agreement 
between theory and observations is not satisfactory, 
and, in particular, the variations from day to day ob- 
served in dark and bright segments and antitwilight 
arch remain unexplained. According to Linlce [29], the 
rigorous theory by Mie-Debye is more suitable for 
the theoretical approach to the twilight colors. How- 
ever, this theory is difficult to apply to the problems 
at hand, because it still involves the assumption of 
spherical particles. In Anew of the new theories of the 
anticorona [6, 20], the consideration of rearward dif- 
fraction should be extended to the theory of the anti- 
twilight arch. 

The theory of the purple light which was recognized 
as a diffraction phenomenon by Kessling [c. 42] was 
established by Gruner [14] along the lines suggested by 
Pernter [42] and others. This theory adequately de- 
scribes the temporal and spatial development of the 
purple hght; the basic ideas may briefly be outlined 
with the aid of schematic Fig. 14. The sun's rays Ro to 
Rz, pass through a dust layer DD' in which they are 
deprived of their short-wave components. While Ro, 
passing through the dense lower layers, and i?3, hav- 
ing the longest path through the dust layer, may be 
completely extinguished, the rays around Rx vnW emerge 
as a reddish beam of light and enter the lower boundary 
of the dust layer again at Pi, where the particles will 



76 



METEOROLOGICAL OPTICS 



be relatively large. These particles may diffract the 
light dominantly at the angle <pi toward the observer 0, 
whose horizon is HH' , and for whom the sun's depres- 
sion is 6. At the higher points P^ and P3, the prevailing 
sizes of the dust particles become successively smaller 
and the diffraction angles <p-i and ipz correspondingly 
larger. Since the incident beam is reddish, the dif- 
fracted rays converging toward will outline a reddish 
area in the sky. The observer sees only those diffracted 
rays that fall in his cone of vision (and are sufficiently 
intense) ; for example, a particle at Pi' of the same size 
as that at Pi and one at PJ of the same size as the one 
at P2, will also diffract light toward 0. It may be noted 
that an observer, for whom the sun is still abo^'e the 
horizon, may see Bishop's ring around the sun. Also, 
the light scattered and diffracted by the dust layer in 
the region of the purple light is sometimes sufficiently 
intense to cause a secondary purple light for an ob- 
server located farther on the night side of the earth 
{i.e., to the right of observer in Fig. 14). The red light 
diffracted by the dust layer and augmented by blue 
light scattered by the air in the region SiS^S^ above 
gives rise to a purplish tone. 




Fig. 14. — Schematic diagram for the purple light. 

From the geometric aspects we can see that the areal 
extent of the purple light depends on the particle size 
distribution, the thickness of the layer, and absorption. 
The latter generally prevents the purple light from 
appearing as a circular arc. The theory does not predict 
the exact color and intensity of the phenomenon; these 
depend on the modification of the incident beam bj^ its 
first passage through the dust layer, its further fate in 
the air below this layer, the specific effect of the dust on 
the beam after re-entrance into the layer, and, finally, 
the modification of the diffracted light on the way to 
the observer, in conjunction with the sky light from 
above. For a homogeneous dust layer, an optimum 
particle concentration and size distribution must exist, 
whereby the red component of the incident sunlight 
experiences a minimum depletion on its first passage 
through the dust layer and produces maximum in- 
tensity of diffracted light when again penetrating the 
layer. 

In general, there are too many unkno\vn variables, in 
particular the scattering function of the dust particles 
and attenuation of the direct rays, to render the problem 
as a whole accessible to an analytical solution, especially 
when multiple dust layers are involved. For the present, 
it appears most expedient to provide reliable observa- 



tional material by means of which the available theories 
may be checked more adequately. In order to eliminate 
from such material all the subjective variables that are 
involved in visual observations, only objective methods 
of observation should be employed. The design of the 
spectrophotometric equipment should incorporate the 
features of very high sensitivity, to enable the use of 
filters with narrow transmission bands, and of rapid 
response, so that the major portions of the sky area 
could be scanned within a few minutes. By means of a 
wide station network, the question regarding the cause 
of asymmetric twilight phenomena that have been var- 
iously attributed to the shape of the atmosphere as a 
whole or the slope of the tropopause [14] could be an- 
swered. The problem of the height of the effective layers 
of the atmosphere and of the shape of the ray envelope 
could be approached by means of airborne photometric 
instruments to furnish vertical cross sections of the light 
flux at various altitudes along a latitudinal line to repre- 
sent various sun's depressions. Spectrophotometry of 
clouds of known height may furnish information on the 
geometrical and optical properties of the sun's rays 
tangent to the earth's surface. 

As regards determination of the terrestrial or possibly 
cosmic origin of dust layers [11, 14] that periodically 
produce striking twilight phenomena, only a long-range 
observational project on an international basis will lead 
to success. 

SCATTERING OF LIGHT IN THE ATMOSPHERE 

Scattering is the deflection of light quanta in a trans- 
parent medium such as the atmosphere. The atoms and 
molecules of the gaseous constituents cause the quanta 
of the incident light beam to be scattered more or less 
in all directions. In addition, there is scattering by 
minute particulate suspensions such as condensation 
nuclei. Wlien a beam of this scattered light encounters 
further matter, it is again subject to (multiple) scat- 
tering; however, the contribution of multiple scattering 
to the total intensity of scattered light is small, except 
in very turbid air or in the absence of primarily scat- 
tered light, {e.g., in the case of the dark segment). 

The classical theory by Rayleigh [c. 21] was found to 
be only in approximate agreement with pertinent ob- 
servations [c. 42]. The later theory by Mie and Debye 
[c. 29], which contains Rayleigh's theory as a limiting 
case, is more general, but difficult to apply to atmos- 
pheric scattering because it requires a laiowledge of 
specific constants, the distribution, and concentration 
of the scattering substances. For a thorough summary 
of the theories of scattering as well as of methods and 
results of observations, the reader is referred to the work 
by Linke [29].=* 

It was shown that the scattering process was involved 
in some of the previously discussed optical phenomena; 
its more immediate manifestations are much less spec- 
tacular, but nevertheless of great practical importance. 
The essential consequences of scattering are: The restric- 



9. See also Chap. 7 on "Die kurzwellige Himmelsstrahlung" 
in the same volume, pp. 339-415. 



GENERAL METEOROLOGICAL OPTICS 



77 



tions in visual range; the polarization of sky light; the 
depletion of direct sunlight; and the luminance of the 
sky in daytime. Only some aspects of sky luminance 
will be briefly mentioned here, as the other topics are 
treated elsewhere in this Compendium.'" 

The luminance of the sky represents a considerable 
portion of that direct sunlight which has been depleted 
in its passage through the atmosphere. A practical 
aspect of this luminance is the resultant illumination 
without which the earth's surface \vould be in darkness 
except where reached by direct or reflected sunlight. 
The most obvious characteristic of the sky's luminance 
is its blue color which is caused by the preference of the 
scattering process for the shorter wave lengths of the 
incident radiation. Far from being a pure blue, the color 
is composed of other wave lengths to an extent that 
varies with the state of atmospheric turbidity, because 
with increase in size of the scattering particles the longer 
wave lengths increasingly participate in the scattering 
process. In the sky light, the ultraviolet component, 
whose intensity may exceed that of the direct sunlight, 
has biological (erythematous and bactericidal) and tech- 
nological (dye-fading, photographic) effects. 

The luminance of the sky is significant from a meteo- 
rological viewpoint because it enters as a factor in the 
appraisal of the atmospheric radiation balance and 
serves as a criterion of the turbidity of the air. In this 
respect, even mere estimations of the variations in the 
sky blue have been shown to be of practical value.'' 

REFERENCES 

1. Archenhold, G., "Untersuchungen liber den Zusammen- 

hang der Haloerseheinungen mit der Sonnentatigkeit." 
Beitr. Geophys., 53: 395-475 (1938). 

2. Beocks, K., "Vertikaler Temperaturgradient und ter- 

restrische Refraktion, insbesondere im Hoohgebirge." 
Verojf. meteor. Inst. Univ. Berlin, Bd. 3, Nr. 4 (1939). 

3. "Eine Methode zur Beobachtung des vertikalen 

Dichte- und Temperaturgefalles in den bodenfernen 
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4. "Lokale Untersehiede und zeitliche Anderungen der 

Dichteschichtung in dei' Gebirgsatmosphare." Meteor. 
Z., 57:62-73 (1940). 

5. Bruche, E., und Bruche, D., "tjber die Photometrie von 

Sonnenringen." Meteor. Z., 49: 289-294 (1932). 

6. BucERius, H., "Theorie des Regenbogens und der Glorie." 

Optik, 1: 188-212 (1946). 

7. CouDER, A., "Mesure photographique de I'agitation at- 

mosph^rique des images stellaires." C. R. Acad. Set., 
Paris, 203: 609-611 (1936). 

8. Dember, H., und Uibe, M., "Uber die scheinbare Gestalt 

des Himmelsgewolbes." Ber. sacks. Ges. {Akad.) Wiss., 
69: 139-148 (1917). 

9. "tJber die Gestalt des sichtbaren Himmelsgewolbes." 

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14. 



15 



10. Consult articles by W. E. K. Middleton, Z. Sekera, 
S. Fritz, and E. O. Hulburt. 

11. See H. and M. Neuberger, "Color Memory in Cyanom- 
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ences there. 



11. DoENO, C, "Dammerungsbeobachtungen Herbst 1911 bis 

Anfang 1917." Meteor. Z., 34: 153-165 (1917). 

12. EscLANGON, E., "Sur les refractions gdod(5siques." C. R. 

Acad. Sci., Paris, 216: 137-1.39 (1943). 

13. Grunee, p., "Photometrie des Purpurlichtes." Beitr. 

Geopkys., 50: 14.3-149; 51: 174-194 (1937). 

— "Dammerungserscheinungen," Handh. Geopkysik, Bd. 
8, Kap. 8, SS. 432-526. Berlin-Zehlendorf, Gebriider 
Borntrager, 1942. 

— und Klee, T., "Numerische Berechnung der Helligkeit 
des Himmels im Sonnenvertikal." Helv. phys. Acta, 
11: 513-530 (1938). 

16. Gruner, p., und Klein^brt, H., "Die Dammerungser- 

scheinungen." Prohl. kosm. Physik, Bd. 10. Hamburg, 
H. Grand, 1928. 

17. HiLLERs, W., "tJber eine leicht beobachtbare Luftspie- 

gelung bei Hamburg und die Erklarung soldier Erschein- 
ungen." UnterrBl. Math. Naturw., 19: 21-38 (1913). 

18. Hulburt, E. O., "The Brightness of the Twilight Sky and 

the Density and Temperature of the Atmosphere." 
/. opt. Soc. Amer., 28: 227-236 (1938). 

19. "The Green Segment Seen from an Airplane." /. 

opt. Soc. Amer., 39: 409 (1949). 

20. HuLST, H. C. VAN DE, "A Theory of the Anti-ooronae.'' 

/. opt. Soc. Amer., 37: 16-22 (1947). 

21. Humphreys, W. J., Physics of tke Air, 3rd ed. New York, 

McGraw, 1940. (See pp. 451-556) 

22. HtJTTENHAiN, E,, "Zur scheinbaren Gestalt des Wolken- 

himmels." Himmelswelt, 46: 94-101 (1936). 

23. IsiMARU, Y., "On the Form of the Firmament, Apparent 

Shape of Cloud and Visual Magnitude of the Sun and 
Moon." /. meteor. Soc. Japan, 4: 3-10 (1926). 

24. Ives, R. L., "Meteorological Conditions Accompanying 

Mirages in the Salt Lake Desert." /. Franklin Inst., 
245: 457-473 (1948). 

25. Jeffreys, H., "The Shape of the Sky." Meteor. Mag., 

56: 173-177 (1921). 

26. Jensen, C, "Atmospharisch-Optische Messungen in II- 

menau." Beitr. Geophys. 35: 166-188 (1932). 

27. Link, F., "L'^clairement de la haute atmosphere et les 

tables cr^pusculaires de M. Jean Lugeon." C. R. Acad. 
Sci., Paris, 199: 303-305 (1934). 

28. und Sekeea, Z., "Dioptrische Tafeln der Erdat- 

mosphare." Publ. Prazske Hvezd&rny, No. 14, pp. 1-28 
(1940). 

29. Linke, F., "Die Theorie der Zerstreuung, E.\tinktion und 

Polarisation des Lichtes in der Atmosphare." Handh. 
Geopkysik. Bd. S, Kap. 5, SS. 120-238. Berlin-Zehlendorf, 
Gebriider Borntrager, 1942. 

30. Lunbburg, R. K., Mathematical Analysis of Binocular 

Vision. Princeton, Princeton University Press, 1947. 

31. Meggers, W. F., and Peters, C. G., "Measurements on 

the Index of Refraction of Air for Wave Lengths from 
2218 A to 9000 A." Bull. nat. Bur. Stand., 14:697-740 
(1919). 

32. Mendelssohn, T., "Photometrie des Purpurlichtes." Rev. 

Fac. Sci. Univ. Istanbul {Istanbul U niversilesi Fen 
Fakultesi Mecmuasi), Ser. A, 6: 94-115 (1941). 

33. und Dember, H., "Uber die Bewegung des Erdsehat- 
tens in der Atmosphare." Rev. Fac. Sci. Univ. Istanbul- 
{Istanbul Universitesi Fen FakiiUesi Mecmuasi), N. S. 
4: 1-30 (1939). 

34. Meyer, R., "Die Haloerseheinungen." Probl. kosm. Pky- 

sik, Bd. 12. Hamburg, H. Grand, 1929. 

35. "Der 'Griine Strahl.'" Meteor. Z., 56: 342-.346 (1939). 

36. "Optische Erscheinungen in der Atmosphare" in 

FIAT Rev. German Sci. 1939-1946, Meteorology and 



78 



METEOROLOGICAL OPTICS 



Physics of the Atmosphere, R. Muggb, sen. author. Off. 
Milit. Govt. Germany, Field Inform. Agencies, Tech. 
Wiesbaden, 1948. (See pp.' 73-81) 

37. Miller, A., Investigations of the Apparent Shape of the 

SkT/. B. S. Thesis, The Pennsylvania State College, 
October 1943. 

38. and NEtrBEBGBR, H., "Investigations into the Ap- 
parent Shape of the Sky." Bull. Amer. meteor. Soc., 26: 
212-216 (1945). 

39. Neubbrgeb, H., "tlber die Beziehung zwischen der Son- 

nentatiglceit und dem Auftreten von Haloerscheinun- 
gen." Beitr. Geophys., 51: 343-364 (1937). 

40. "Some Remarks on the Problem of the Dark Seg- 
ment." Bull. Amer. meteor. Soc., 21: 333-335 (1940). 

41. Pepplbb, W., "ttber Glorien und Halos." Z. angew. Meteor., 

56:173-186 (1939). 

42. Pernter, J. M., und Exner, F. M., Meteorologische Optik, 

2. Aufi. Wien u. Leipzig, W. Braumiiller, 1922. 

43. PozDi}NA, R., "Das Funkeln der Sterne und zwei damit 

zusammenhangende, bisher unzureichend geloste Prob- 
leme." Beitr. Geophys., 41: 203-208 (1934). 

44. PuTNiNS, p., "Der Bogen von Parry und andere unechte 

Beriihrungsbogen des gewohnlichen Ringes." Meteor. 
Z., 51:321-331 (1934). 

45. Ramachandran, G. N., "The Theory of Coronae and of 

Iridescent Clouds." Proc. Ind. Acad. Sci., (A) 17: 202- 
218 (1943). 

46. RiGGS, L. A., and others, "Photographic Measurements 

of Atmospheric Boil." /. opt. Soc. Amer.. 37: 415-420 
(1947). 



47. ScHWEBDTFEGER, W., "Wasserglorien und Eisglorien." 

Meteor. Z., 55: 313-317 (1938). 

48. SiBDENTOPF, H., und Holl, H., "Helligkeitsabfall und 

Farbanderung wahrend der Dammerung." Beichsber. 
Physik (Beih. z. Phys. Z.) 1 (1): 32-40 (1944). 

49. Skreb, S., "Zur Kritik der sogenannten Referenzflache." 

Meteor. Z., 50: 310-311 (1933). 

50. Smosarski, W., "Dammerungsfarben-Intensitat in den 

Jahren 1913-1936." Beitr. Geophys., 50: 252-263 (1937). 

51. "Intensity et polarisation de la lumiere atmosph^- 

rique." Ann. Geophys., 2: 1-18 (1946). 

52. VissBE, S. W., "Sunspots and Halos at Batavia." Beitr. 

Geophys., (Koppen-Band I), 32: 192-201 (1931). 

53. "Die schiefen Bogen der Gegensonne." Meteor Z., 

53: 336-340 (1936). 

54. and Verstelle, J. T., "Groene Straal en Kim- 

duiking." Hemel en Dampk., 32: 81-87 (1934). 

55. Wahl, E., "Die Bildruhe bei astronomischen Beobacht- 

ungen, ein Turbulenzkriterium." Beitr. Geophys., 58: 
370-384 (1942); and .59: 49-73 (1943). 

56. Wegener, K., "Bemerkungen zur Refraktion." Beitr. 

Geophys., 47: 400-408 (1936). 

57. Whipple, F. J. W., "Rainbow with Vertical Shaft." 

Meteor. Mag., 71: 259-260 (1936). 

58. WooLARD, E. W., "The Geometrical Theory of Halos." 

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190-192, 301-302 (1937); 69: 260-262 (1941). 

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und die astronomische Inflexion in ihr." Beitr. Geophys., 
31: 83-118 (1931). 



POLARIZATION OF SKYLIGHT 

By ZDENEK SEKERA 
University of California, Los Angeles 



Introduction 

Since the discovery by Arago in 1809 that the hght 
of the clear sky is polarized, interest in the problems 
of skylight polarization has varied greatly. At first, 
attention was concentrated more on the development 
of a suitable measuring technique to determine the 
magnitude of the polarization and its distribution over 
the sky. Arago first discovered a neutral point, named 
after him the Arago point, where the polarization dis- 
appears, about 20° above the antisolar point. The other 
neutral points were discovered in 1840 about 20° above 
the sun by Babinet and below the sun by Brewster. 
Because of the simplicity of the determination of neu- 
tral points, more attention was paid later on to their 
study and soon a complete picture of diurnal, seasonal, 
and secular variations in the position of the Arago and 
Babinet points was obtained. 

Arago's discovery of a point of maximum polariza- 
tion 90° from the sun in the sun's vertical was followed 
during the next two or three decades by studies of the 
variability of the maximiun polarization at this point 
(Bernard, Rubenson, Crove, Cornu, etc.). 

For several reasons, interest in atmospheric polariza- 
tion culminated at the end of the last century. The 
photopolarimeter, constructed by Cornu in 1882, rep- 
resents the highest point in the development of the 
visual measurement of polarization. The accxunulated 
results of polarization measurements gave rise to a 
series of attempts to explain the observed facts theo- 
retically, culminating in Lord Rayleigh's theory of 
molecular scattering. 

The famous eruption of Ivi-akatao (1883) showed the 
extraordinary sensitivity of skylight polarization to the 
presence of volcanic dust in the upper atmosphere. For 
several decades thereafter, the investigation of polari- 
zation was considered almost exclusively as a suitable 
tool for the study of perturbations of a similar kind. 
But since the last eruption of Katmai in 1912 no anom- 
alies of this type occurred, and the interest in problems 
of atmospheric polarization rapidly decreased. Smaller 
fluctuations in the polarization were studied and the 
measurements were extended to rather narrow spectral 
ranges. Surprisingly, a great discrepancy was found 
between the results of different authors, and the only 
possible explanation for this is a large variability of the 
dispersion of polarization (variation with the wave 
length) with the size and number of scattering par- 
ticles. As these quantities vary greatly with local con- 
ditions (weather, season, etc.), the corresponding vari- 
ations in polarization follow. But if the presence of 
scattering particles of different size is admitted, the 



question arises whether it is the secondary scattering 
or the presence of larger particles (excluded by the 
assumptions of Rayleigh's theory) which is responsible 
for the observed deviations of the atmospheric polari- 
zation from expectations based on theory. 

After Ahlgrimm's successful attempt to compute the 
effect of secondary scattering, in which he explained 
most of the facts better than he explained the observed 
variations. Milch in 1924 presented a theory in which 
the secondary scattering was neglected and the effect 
of larger particles was considered responsible for the 
deviations from Rayleigh's theory. The close relation- 
ship between Linke's turbidity factor and the degree 
of polarization, predicted by Milch's theory, was dem- 
onstrated in 1934 by Blickhan from simultaneous ob- 
servations of polarization and turbidity. But he ob- 
tained much better agreement between the observed 
and theoretical values of the maximum polarization 
when he considered the effects of both secondary scat- 
tering and the presence of larger particles. 

Even though Blickhan's results clearly pointed the 
way for further investigations, no appreciable increase 
of interest in this direction has followed. The reason 
for a recent slight increase of interest in problems of 
skylight polarization is quite different. First, the intro- 
duction of objective methods, such as the photoelectric 
techniques in photometry, showed the possibiUty of 
more accurate and systematic measurements. Then, 
after the first attempts to use optical methods for the 
exploration of the upper atmosphere, attention was 
brought to the polarization of the skylight during twi- 
light and during the night. The great technical difficul- 
ties in the measurement of the extremely low intensi- 
ties of the skylight during these hours led even to the 
use of searchlight beams in the study of atmospheric 
scattering. But since, during twilight, direct illumina- 
tion from the sun is less and less intense, the secondary 
and multiple scattering become more and more impor- 
tant. And just at the present moment when there is a 
need for computation of the effect of secondary and 
multiple scattering, recent research in theoretical astro- 
physics offers help. The scattering by free electrons 
produces polarization of stellar radiation, the theoreti- 
cal study of which led Chandraselchar to develop an 
excellent method for computing multiple scattering 
exactly, suitable for application to the problems of 
atmospheric polarization. Thus we are now in a posi- 
tion to use a highly developed modern experimental 
technique, together with excellent theoretical tools for 
solving many problems of skylight polarization in such 
a manner that very useful information can be ob- 
tained. 



79 



80 



METEOROLOGICAL OPTICS 



Measurement of Skylight Polarization 

In the measurement of skylight polarization, there 
occur two different problems: measurement of the de- 
gree of polarization and measurement of the position 
of neutral points. 

The visual measurements of the degree of polariza- 
tion were highly developed by Cornu in his photopo- 
larimeter [17], and slightly improved by Martens [42]. 
This photopolarimeter contains a Wollaston prism as 
polarizer and a Nicol prism as analyzer. Both prisms 
can be rotated around the same axis and their mutual 
position and the position of the polarizer can be read off. 

With the analyzer fixed 45° to the principal axis of 
the Wollaston prism the plane of polarization is deter- 
mined by the position of the Wollaston prism in which 
both halves of the field in the eyepiece have the same 
intensity. The plane of polarization is then inclined 
45° from the principal axis of the Wollaston prism. If 
the Wollaston prism is now rotated by 45°, one half of 
the Wollaston prism transmits the intensity normal to 
the plane of polarization, the other the intensity in the 
plane of polarization. While the Wollaston prism is 
kept fixed the Nicol prism is rotated until both halves 
of the field have the same intensity. The degree of 
polarization P is then equal to cos 2w, if co is the angle 
between the principal plane of the Wollaston and of 
the Nicol prism, usually readable by means of a scale 
outside of the instrument. 

The precision of this method was discussed by Smo- 
sarski [62] and found to be most accurate for large 
values of P; for small values of P this method requires 
some modification. Errors due to incorrect settings of 
the polarizer or of the analyzer can be eliminated by 
taking successive readings with the prism in the posi- 
tion 90°, 180°, and 270° from the original position. In 
this way a precision of 1-2 per cent can easily be 
reached, provided the illumination of the field in the 
eyepiece is sufficient to enable one to distinguish the 
unevenness of its halves. Another disadvantage is a 
relatively long time interval (about six minutes) nec- 
essary for all settings and readings. Because of the 
failure of this method in the case of rapid fluctuations 
in polarization or of inadequate illumination (during 
twilight or night), visual methods are being replaced 
more and more by objective methods. 

Because of the cumulative effect during longer ex- 
posures, photographic photometry is often used when 
the illumination is inadequate. By means of a Wollaston 
prism a double picture of the measured field is obtained, 
and the degree of polarization is computed from the 
ratio of the intensities of the separate pictures. The 
precision of this method is limited by the precision in 
setting the principal section of the prism in or nonnal 
to the plane of polarization and in keeping it in this 
direction during the exposure. Especially during the 
night, when the illumination is very weak, this pro- 
cedure is very difficult. Another limitation of the photo- 
graphic method is the great variability of the pho- 
tographic material, which makes necessary a special 
sensitometric arrangement for the determination of a 



characteristic curve for each exposure. For exact meas- 
urement, a standard intensity scale must be simul- 
taneously exposed on the plate or fihn, and after de- 
velopment, the characteristic curve from the measured 
intensities is determined by a visual or photoelectric 
photometer. This procedure, unfortunately omitted by 
several authors, makes photographic polarization meas- 
urement rather complicated without any gain in pre- 
cision over the visual method (the accuracy seldom 
exceeds 5 or 10 per cent). However, if this procedure is 
not followed, the results are quite unreliable. On the 
other hand the photoelectric method seems to be more 
convenient for an objective polarization measurement. 
It offers not only the possibility of a fast and contin- 
uous measurement but also of measurement at low 
intensities. The continuous measurement can easily be 
made by measuring the intensity of light passing 
through a rotating Nicol prism or other analyzer [57]. 
If the prism rotates around its axis with a constant 
angular speed u, then the intensity of the photoelec- 
tric current from the photocell situated behind the 
prism is proportional to M/„ -+- Ip cos^ wt, if the time 
is counted from the moment when the principal plane 
of the prism (the plane of transmitted vibrations) is 
normal to the plane of polarization of the measured 
partially polarized light, the polarized and unpolarized 
components of which have intensities Ip and /„, re- 
spectively. For light of greater intensity the current 
can be recorded continuously, and the degree of polar- 
ization detennined from two intensities (maximmn and 
minimum) if the period and the decrement of the galva- 
nometer or other recording system used is known. If 
the rotation of the prism is uniform and sufficiently 
slow, the direction of the polarization plane can also 
be determined by a very simple arrangement. By a 
suitable choice of the recording system even very rapid 
fluctuations in the polarization can be studied in this 
manner. The measurement of the polarization for low 
intensities can also be made without any basic diffi- 
culty if very sensitive photocells (photomultipliers) are 
used or if the photoelectric current is properly ampli- 
fied. Since a-c amplification is more effective, it is 
desirable to produce photoelectric alternating current, 
for which purpose fast rotation of the prism can con- 
veniently be used. 

Because the spectral sensitivity of the human eye 
differs from that of the photocell or the photographic 
material, the results of the objective methods will in 
general be different from that of the visual measure- 
ment. It can be shown [58] that, if there is no dispersion 
of the polarization, that is, if P is constant for all wave 
lengths, there will be no difference in the results of 
these different methods. But if the dispersion occurs, 
that is, P is different for different wave lengths, the 
difference between P measured by different methods 
will be greater, the greater the dispersion of the polari- 
zation. Since the dispersion depends upon the turbidity 
of the atmosphere, the difference between the results 
obtained by the different methods may vary appreci- 
ably from day to day. 

The measurement of the position of neutral points is 



POLARIZATION OF SKYLIGHT 



81 



much simpler. Their elevation above the horizon is 
measured by standard procedures (usually by a pen- 
dukmi quadrant or a theodolite) ; for finding the neutral 
point any type of polariscope can be used. The most 
convenient type is the Sa\'art polariscope and its modi- 
fications. The main part of the polariscope is Savart's 
double plate (two plates of the same thickness cut 
under 45° from, the optical axis of a quartz or any 
unia.xial crystal; one of them turned through a right 
angle from the other). If a polarized light passing 
through the double plate is observed through an ana- 
lyzer with the plane of polarization bisecting the angle 
between the principal planes of transmittance of the 
plate, parallel color fringes appear. They have a dark 
or bright central band, depending on whether the in- 
cident light is polarized at right angles or parallel to 
the plane of tran.smittance of the double plate. The 
fringes disappear if the incident light is unpolarized. 
The modifications of Savart's polariscope differ with 
the t.ype of analyzer used. In the original model a 
tourmaline plate was used. Its great disadvantage was 
a strong absorption resulting in a dark green color of 
the field. By vising a Nicol or similar prism this dis- 
advantage can be removed, but the field is then verj^ 
small. Much larger fields and an extraordinary bright- 
ness of fringes can be reached in Voss's modification [69] 
with a Wollaston prism as analyzer. By a suitable ad- 
justment of the thickness of the double plate and the 
Wollaston prism, the deviation of the ordinary and 
extraordinary rays emerging from the prism can be 
made exactly equal to the angular distance of the in- 
terference fringes. In this way the fringes in the ordi- 
nary and extraordinary system of rays coincide and 
their intensity is doubled. Because of its great lumi- 
nosity the Voss polariscope is very useful for measur- 
ing neutral points late after sunset. Its colorless field 
makes it particularly useful for measurements within a 
narrow spectral zone. The advantage of a colorless field 
can also be achieved by using a polaroid plate as ana- 
lyzer [45]. 

If the polariscope is set up with fringes parallel to 
the sun's vertical in the vicinity of a neutral point, the 
dark central band above the point continues as a bright 
one below with an interruption in the middle in the 
exact position of the neutral point. The elevation of 
this point is then measured. The position of the inter- 
ruption in the fringes can also be determined photo- 
graphically [6]. 

Distribution and Magnitude of the Polarization over 
the Sky 

As already mentioned, the degree of polarization of 
skylight reaches its maximum in the sun's vertical, 90° 
from the sun. Mean values of a large number of meas- 
urements of the polarization at this point taken in 
different years and at different places, agree relatively 
well, showing a decrease of the degree of polarization 
with increasing elevation of the sun (Fig. 1). Measure- 
ment of polarization at the zenith was introduced by 
.Jensen [31| and perfoi'med by several authors because 
of the simplicity of having a fixed position of the ob- 



served direction independent of the sun's elevation. 
With the sun at the horizon, the zenith coincides with 
the point of maximum polarization. With the sun above 
the horizon, the polarization at the zenith decreases 
rapidly as the point of maximum polarization descends 



0.9 



z 
o 



0.7 



< 



o 

0. 




0.5 



SUN'S ELEVATION 
Fig. 1. — Polarization at the point of maximum polarization 
(in the sun's vertical, 90° from the sun) for different sun's 
elevations h.. Observed values (Dorno, Gockel, Tichanow.ski) 
compared with theoretical values (secondar}' scattering ac- 
cording to Ahlgrimm). 



1.0 r 



z 
o 

I- 
< 

a. 
< 



0.5 




0° 20° 40° 

SUN'S ELEVATION 
Fig. 2. — Polarization at zenith for different sun's elevations 
/«.,. Theoretical values (I — Raj-Ieigh's theory of primary scat- 
tering, II — secondary scattering according to Ahlgrimm) com- 
pared with observed values (Tichanowski, Gockel, Jensen, 
Dorno). 

to\Aards the horizon. The dail.y variation of the polari- 
zation at the zenith has thus the same character as 
that of maximum polarization, but with a much larger 
range of variation, as may be seen in Fig. 2. The meas- 
urement of polarization at the zenith, extended for 
negative sun's elevations /u-, gives an interesting residt: 
the maximum polarization at the zenith is reached for 



82 



METEOROLOGICAL OPTICS 



a sun's elevation between —2° and —4°. The increase 
of polarization for hs < was found to be more rapid, 
the lower the value of the polaiization at hs = 0. 

The distribution of the polarization over the sky was 
studied extensively by Dorno [22]. In a stereographic 
projection with the sun at its pole, the lines of equal 
polarization are nearly concentric circles around the 
sun. For corresponding P, the circles on the sun's side 
are closer to the equator (the line of maximum polari- 
zation) than on the antisolar side, showing a slight 
asymmetry of P in the sun's vertical, a fact studied 
and proved by Smosarski [62]. The distribution — sur- 
prisingly — varies very little with the elevation of the 
sun above the horizon. 

The position of the plane of polarization was also 
measured and, at first, lines were drawn parallel to the 
direction of this plane. Later on they were replaced by 
the lines connecting points with the same inclination of 
the plane of polarization to the vertical (polarization 
isoclines). Since the inclination 45° to the vertical, 
called also a neutral line or Busch lemniscate, can 
easily be measured by the interruption of the vertical 
fringes in a polariscope (similar to the neutral points), 
it was studied extensively by Dorno [22] and Mentzel. 
Mentzel's measurements were recently revised by Dalh- 



fore suggested by Jensen [30] as reliable indicators of 
atmospheric turbidity. Comparing the mean values for 
winter and summer from a period with a fairly normal 
condition, Jensen concluded that, with increasing tur- 
bidity, (1) the antisolar distances of the A -point in- 
crease, (2) the difference between the maximum and 
the secondary miniminn for the A-point increases, and 
(3) the position of the minimimi in the ^ -point curve 
is shifted to the negative hs. The variations in the dis- 
tances of the £a-point do not follow such simple rules, 
being more sensitive to the conditions at much higher 
levels which are unaffected by the seasonal variations. 
Neuberger [45] studied the interrelationship between 
the extremes in the ^ -point curve and found a very- 
high correlation (-1-0.95 ± 0.01) between the difference 
in (2) and the distance of the ^-point for hs = 10.5° 
or 13.5°, suggesting that a single measurement of the 
A-po'mt distance for these values of hs can be used as 
an indicator of the turbidity. When he compared the 
distance of the 4-point at hs = 10.5° with the direct 
measurement of solar radiation, Neuberger found an 
increase of this distance with decreasing intensity of 
solar radiation; this would agree with the statement in 
(1) above. 
As another indicator of turbidity, the difference be- 



Table I. Difference Between A-point and Ba-point Distances (in degrees) 



Hamburg, 1909-11. 
Arnsberg, 1909-11 . 
Davos, winter 1911 
Davos, spring 1912 



5.5° 



5.9 
6.3 
0.1 
0.9 



h, = 4.5° 



5.0 
5.6 
0.3 
0.0 



h, = 3.5° 



4.1 
4.6 
0.5 
1.0 



: 2.5° 



3.3 
3.8 
0.6 
0.6 



1.5° 



2.3 
2.9 
0.1 
0.1 



h, = 0,5° 



1.4 

2.1 

-0.1 



h, = -0.5° 



0.9 

1.6 

-0.2 



kamp and Kantus [20] and discussed with respect to 
the possibility of using the shape or the area inside the 
Busch lemniscate as a measure of the turbidity. 

More attention has been devoted to the measurement 
of the position of neutral points than to the measure- 
ment of the degree of polarization. The reason for this, 
besides the great simplicity of the measurement, is the 
great variability of these positions, and their greater 
sensitivity to the turbidity of the atmosphere. The 
measurements mostly relate to the Arago and Babinet 
points; the position of the Brewster point has not been 
studied systematically because it is difficult to measure 
(below the sun, close to the horizon). The distance of 
the Ai-ago point from the antisolar point and of the 
Babinet point from the sun vary in a characteristic 
way for small positive and negative elevations of the 
sun. If the distances of these points {A- and £a-points) 
are plotted against the sun's elevations, then the curve 
for the .4 -point shows a minimmn (or a secondary mini- 
mum) for small negative hs, while — under normal con- 
ditions — the 5a-point curve shows a secondary maxi- 
mum (c/. Fig. 3). These extremes in both curves are 
followed by a rapid increase for larger negative h,. The 
position and the values of those extremes (for the Ba- 
point, even the whole character of the curve) change 
greatly with the turbidity; these quantities were there- 



tween the points of the A- and -Ba-point curves for the 
same hs can be used. This difference increases with in- 
creasing turbidity, as is clearly shown in Table I, where 
the values of this difference, measured in a turbid at- 
mosphere (Hamburg, Arnsberg), are compared with 
those measured in a much less turbid atmosphere 
(Davos). 

Quite distinct is the effect of ground reflection on the 
curve of A-point distances. The maximuni, which at a 
land station is usually very flat and is observed around 
hs = 12.5°, shifts to smaller sun's elevations and de- 
creases in value in the vicinity of large water surfaces 
[30]. If the reflection is strong, new neutral points ap- 
pear, either below the ordinary points (as observed by 
Rubenson [54] below the jBa-point, and by Jensen [3] 
and Neuberger [44] below the A-point) or on both sides 
of the sun at the same elevation (Soret [63]). In a 
polariscope the fringes are visible even over the water 
surface, in the sun's vertical, with a dark central band 
(positive); in other directions they show a bright cen- 
tral band (negative). In a position closer and closer to 
the observer as the direction approaches 90° from the 
sun's vertical, the negative fringes change rapidly into 
the positive, suggesting the existence of a series of neu- 
tral points, or better, the existence of a transition zone 
(Umkehrzone, Jensen [3, 30]) between the negative po- 



POLARIZATION OF SKYLIGHT 



83 



larization (the plane of polarization horizontal) on the 
horizon and the positive polarization (the plane of 
polarization vertical) over the water surface around 
the observer. Similar phenomena over land were ob- 
served by Brewster as early as 1841. 

The biggest anomalies in the described distribution 
of polarization were observed after the volcanic erup- 
tions of 1883-1885, 1902-1903, and 1912-1914. The 
effect of the volcanic dust present in the atmosphere 
could be noticed in the extraordinarily low values of 
the degree of polarization. In 1884, Cornu [18] observed 
the rapid decrease of the maximum polarization from 
0.75 to less than 0.48; Dorno's mean values for the 
zenith and h^ = 0° were P = 0.557 for 1913 and P = 
0.739 for 1915. A very rapid increase of P during twi- 
hght also appeared (Kimball [38]). Much larger effects 
could be observed in the positions of neutral points. 

1911 1912 



UJ 

o 

< 
1- 
Ol 

O 

< 

_1 




+ 3.5' 



•1.5' 



-0.5° H-2.5° 

RUN'S ELEVATION 
Fig. 3. — Distance of the Babinet point {Ba) from the sun 
and of the Arago print {A) from the antisolar point for different 
sun's elevations h^. (Normal conditions — 1911; after volcanic 
eruption of Katmai — 1912). 

Besides the ordinary A- and Ba-points, Cornu [18] ob- 
served four neutral points symmetrically situated at 
the same elevation on both sides of the sun and the 
antisolar point. The distances of the ^-point and Ba- 
point increased; the largest increase, however, was ob- 
served in 1902, and was more pronounced for the Ba- 
point, as was also observed to be true in 1912. In Fig. 3 
the mean values are compared for years with and with- 
out this effect; with respect to the ^ -point, the effect 
mentioned above, namely the increase of the distance, 
is clearly shown and the shift of minimum towards 
larger solar depressions also appears. The effect on the 
Sa-point curve is so great that its character is com- 
pletely changed; the curve is shifted to the other side 
of the A -point curve. 

Theory of Skylight Polarization 

The first correct step toward the explanation of sky- 
light polarization was made by Lord Rayleigh [50] in 



1871. He explained skylight polarization as the scatter- 
ing of sunlight on molecules and submicroscopic par- 
ticles with diameters much smaller than the wave 
length of the incident ray of light. If it is assumed that 
the scattering process takes place only once (primary 
scattering) and if refraction is neglected, the degree of 
polarization of partially polarized light in the direction 
ip from the sun's rays. 



P = (sin2^5)/(l -f cosV), 



(1) 



is a function of v only. The maximiun polarization oc- 
curs in the direction 90° from the sun, where the light 
is totally polarized (P =1). There are two neutral 
points: one in the direction towards the sun, and one 
toward the antisolar point. Elsewhere the light is par- 
tially polarized with the plane of polarization defined 
by the sun, the observer, and the observed point in the 
sky. The theory agrees quite well with the observations 
with respect to the position of the point of maximum 
polarization and of the plane of polarization. But it 
does not explain the partial polarization at the point 
of maximum polarization and the existence of the ob- 
served neutral points. The assiunptions of Rayleigh's 
theory are apparently not satisfied exactly in the atmos- 
phere. The scattering particles are not isotropic and 
the theory should be modified for anisotropy of mole- 
cules (Cabannes [12]). The expression (1) then takes 
the form 

P = (1 - a) (sin^ ^)/(l + cos^ p+a sin^ <p) (2) 

in which a = 0.043 is the coefficient of depolarization. 
Thus the maximum polarization at <p = 90° is P = 
0.922, but the position of the neutral points is not 
affected by the anisotropy of molecules. 

The effect of secondary scattering, omitted in Ray- 
leigh's theory, was studied as early as 1880 by Soret 
[64]. In the first approximation he considers only the 
light scattered by particles assumed uniformly dis- 
tributed in a ring around the horizon. In the center of 
the ring, with the sun at the horizon, the intensity of 
the light scattered by all particles in the ring has the 
components 



4 = T^b/i = 4/8, ij = 37r6/4 = 3h/S, 
Zj = 2irb, (b = const). 



(3) 



Since the vertical component is predominant, the scat- 
tered light is negatively polarized in all directions along 
the horizon. In the direction 90° from the sun the com- 
ponent ix is added to the primary scattered light, that 
is, the light is partially polarized. The neutral points 
are displaced to the positions where the positive polari- 
zation due to the primary scattering is compensated by 
the negative polarization of particles in the ring aroimd 
the horizon. The distances of neutral points can be 
computed from relation (2) {cf. van de Hulst [68]). If 
Pi and P denote the intensities of primary scattered 
light normal or parallel to the plane of polarization, 
and -Si and S the intensities of secondary scattered 
light from the ring around the horizon, then a neutral 



METEOROLOGICAL OPTICS 



point appears in the sun's vertical at the elevation h, 
provided that in this direction 

P,+ Sr = P + S. (4) 

For the sun at the horizon, P/Pi = cos^ h. The intensi- 
ties ^1 and (S are normal to the direction h, and thus 
Si = iy, S = ij, sin^ h + i^ cos^ h, and from (3) 

S/Si = (1 + 7 cos^ h)/3. (5) 

In (5) the intensities can be expressed by the total in- 
tensities (Pi -|- P, (Si -|- S), and then if the ratio R = 
(fSi h <S)/(Pi + P) is known, the elevation of the neu- 
tral point is determined from the equation 

sin^ /i/(l + cos^ h) 

= P(7cos2/i- 2)/(4-f-7cos2/i). (6) 

The most probable value of R lies within the limits 
R = 0.1 and R = 0.2, which gives h = 16.7° and h = 
22.4°, in good agreement with observation. 

Ahlgrimm [7] extended Soret's computation for arbi- 
trary solar elevation, neglecting the extinction and 
assuming only that the distribution of scattering par- 
ticles is the same in all azimuths. The unl^nown dis- 
tribution of scattering particles with height appeared 
in the integrand of integrals which could be evaluated 
by means of the transmission coefficients. Using the 
measured values by Abney,' Ahlgrimm was able to 
compute the degree of polarization due to the primary 
and secondary scattering in any arbitrary direction. 
The values of maximum polarization as a function of 
solar elevation are reproduced in Fig. 1, values of the 
polarization in the zenith in Fig. 2. 

Consideration of secondary scattering thus brings a 
great improvement in the qualitative agreement of the 
theory with observations under normal conditions, but 
a quantitative agreement still cannot be reached. Ticha- 
nowski [66] extended Ahlgrimm's computations, con- 
sidering the anisotropy of molecules and e\'en the re- 
flection from the ground, but without any quantitative 
improvement. The effect of atmospheric extinction and 
refraction was taken into account by Linlc [39]. In such 
a case the integration for secondary scattering cannot 
be performed in any analytic form and requires a tedi- 
ous quadruple numerical or graphical quadrature. Un- 
fortunately the computations were made for the de- 
pressions of the sun for which no observations are 
available yet. 

Comparison of the theoretical curve of the 5a-point 
with that obtained during the period after volcanic 
eruption suggests the presence of another mechanism 
which may be even much stronger than the effect of 
secondary scattering. The appearance of Bishop's ring 
and other twilight phenomena proved the presence of 
larger particles (according to Pernter [47] of a diameter 
from 3.2 X to 6 X) than assumed in Rayleigh's theory. 
The theoretical and experimental investigations of the 
scattering by particles of such a size, by Schirmann 
[55, 56] and later by Blumer [10], showed the possibil- 
ity of neutral points already in the primary scattered 

1. Abney's values are reproduced in [5]. 



light, and led Milch to the idea of using the presence 
of larger particles as an explanation of the deviation of 
the observed values from those given by Rayleigh's 
theory. Neglecting the effect of secondary scattering, 
Milch developed the following expression for the de- 
gree of polarization : 



P = 



mop + iJ.o\p,f{h,, T) 
moip + n) + ti,{^^v)f{K,T)' 



(7) 



where mo and tia denote the number of molecules and 
large particles per unit volume at the ground ; p and ^, 
the intensity of the polarized part of the light scattered 
by molecules and by large particles respectively ; p -|- n 
and ^ + V, the total intensity in both cases of scatter- 
ing; and finally, f{hs, T) is a function of the sun's ele- 
vation and the turbidity coefficient computed from the 
extinction values for different turbidities. This expres- 
sion can explain all observed variation of the polariza- 
tion with turbidity, but its use for the computation of 
P is very limited by the lack of knowledge of the func- 
tions \p and V. Assuming that at the point of maximum 
polarization 4' can be neglected with respect to p, 
Milch determined v from the measured value of P for 
a given /i^, and computed the variation of maximum 
polarization with hs. But the computed values showed 
a systematic deviation from the observed P. 

In continuation of Milch's work, Blickhan [9] studied 
the correlation between the turbidity coefficient and 
the maximum polarization measured simultaneously. 
The values of P lie along a hyperbola P = A/{B -\- Tk) 
in a (P, 7'/,) — diagram {Tk is the turbidity coefficient for 
short-wave radiation, and A and B are constants), in 
good agreement with the simplified formula (7). Ex- 
trapolating P by means of this empirical formula for 
an atmosphere without large particles {T = 1), he ob- 
tained a value of P for /i,, = 50°, which is larger than 
that obtained for /i,, = 32.5°, in agreement with Ahl- 
grimm's computation. From the difference between the 
extrapolated values and those computed by Ahlgrimm, 
assuming further that the light reflected from the 
ground is not polarized, Blickhan was able to compute 
the albedo a = 0.132, which is in good agreement with 
Dorno's values. For the computation of the daily vari- 
ation of maximum polarization he used Milch's pro- 
cedure, but with the difference that in (7) he inserted 
for p and n the values computed by Ahlgrimm. The 
values obtained in this way agreed with the measured 
ones much better than if the effect of the secondary 
scattering had been neglected. Other simultaneous 
measurements of polarization and turbiditj'' were made 

Table II. Polarization at Zenith (per cent of normal 
value) AS A Function of Turbidity 



T 


2.0-2.5 


2.51-3.0 


3.01-3.5 


3.51-4.0 


4.01-5.0 


>5.0 


P 


114.4 


112.0 


104.0 


102.8 


93.2 


68.3 



by Worner [70]. The polarization was measured this 
time at the zenith and was compared with the normal 
values computed by Jensen [2] (Fig. 2). The degree of 
polarization expressed in per cent of normal values 



POLARIZATION OF SKYLIGHT 



85 



shows a close correlation with the turbidity factor, as 
may be seen from Table II. Jensen's normal values 
correspond thus to the turbidity factor 3.9. 

In connection with Milch's and Blickhan's work the 
I'ecent in\'estigation of Tousey and Hulburt [67] should 
be mentioned. The brightness and the polarization of 
the daj'light sky were measured at different altitudes 
up to 10,000 ft. The curves of polarization with height 
showed clearly a much slower rise after a rapid increase 
within the first 2000 or 3000 ft, closely resembling the 
distribution of the turbidity coefficient with height [41]. 
They compared the measured values with theoretical 
values obtained on the assiunption that the secondary 
scattered light is unpolarized, but taking full account 
of the extinction defined by a mean value of the theo- 
retical extinction coefficient 13 = 0.0126 km^^ They 
found that a somewhat better agreement for larger dis- 
tances from the sun can be obtained with p increased 
to 0.017, 0.018, or 0.021 km-i. The systematic devia- 
tions in the vicinity of the sun, expected by the au- 
thors, are caused by the assumption above, eliminating 
the neutral points around the sun. The increase of |S 
proves without doubt the presence of larger particles, 
sufficient to increase the theoretical scattering by about 
35 per cent. The increased values of (3 mentioned above 
correspond to the turbidity coefficient T = 1.35, 1.43, 
and 1.67, respectively. These values are in very good 
agreement with the measured values mentioned above 
[41], indicating the real presence of larger particles 
rather than a systematic error in taking too wide a 
spectral range, as suggested by van de Hulst [68]. In 
the theoretical computation the reflection by the ground 
was taken into consideration and the variation of the 
maximum and zenithal polarization due to the different 
values of the albedo is given in Table III. 



Table III. Effect of Ground 


Reflection 


ON Skylight 


POLABIZATION 


Albedo a 


0.0 


0.1 


0.2 


0.4 


0.6 


Tousey and Hulburt [67] 












P (maximum) : h, = 30° 


0.85 


— 


0.755 


0.667 


0.612 


P (at zenith) : h, = 30° 


0.527 


— 


0.482 


0.439 


0,408 


Chandrasekhar [16] 












P (maximum) : 












h, = 0° 


0.918 


0.903 


0.885 


— 


— 


h, = 13.9° 


0.906 


0.860 


0.801 


— 


— 


h, = 39.8° 


0.906 


0.796 


0.673 


— 


— 


P (at zenith) : 












hs = 0° 


0.918 


0.903 


0.885 


— 


— 


h, = 13.9° 


0.824 


0.779 


0.727 


— 


— 


h, = 39.8° 


0.392 


0.360 


0.315 


— 


— 



The mean value of the measured albedo, a — 0.20, 
was taken for the computation, and for this value the 
theoretical degree of polarization at zenith, P = 0.482 
for hs = 30°, and P = 0.724 for h, = 15° may be com- 
pared with the values of P computed by Ahlgrimm 
(0.469, 0.738) ; and for h„ = 25° the observed value 
P = 0.58 may be compared with the theoretical \'alue 
P = 0.572 (Ahlgrimm 0.558). 

From the discussion above it is quite evident that a 
better quantitative agreement between measurement 



and theory can be achieved when the original Rayleigh 
theory is extended by a consideration of (1) the effects 
of multiple (at least secondary) scattering, extinction, 
and reflection by the ground, and (2) the effect of the 
presence of large scattering particles. The effects men- 
tioned first can lower Rayleigh 's theoretical values to 
the observed values and explain the existence of neu- 
tral points in observed positions; but for the explana^ 
tion of the great variety and magnitude of diurnal, in- 
terdiurnal, seasonal, and secular variations the highly 
variable content of larger particles in the atmosphere 
must be considered. This is more evident if the disper- 
sion of polarization is taken into account. The presence 
of larger particles can best be taken into account in 
the quantitative analysis, however, by separating and 
subtracting the effect of molecular scattering as a sim- 
pler and more nearly constant factor. For this purpose 
the recent theoretical investigations of similar problems 
in astrophysics offer excellent help. In a verj^ elegant 
way, Chandrasekhar succeeded in reducing the exact 
solution of quite general multiple scattering to a solu- 
tion of two relatively simple integral equations of a 
form suitable for successive iteration. Once the solu- 
tion of these equations is known, the exact problem ii 
solved. The great advantage of this method is not only 
that the extinction is very simply taken into account, 
but mainly that the effect of ground reflection can be 
included, as proposed by van de Hulst, and that the 
method can be extended for a more general law of scat- 
tering than in Rayleigh's theory [13, 14, 15]. 

Chandrasekhar has recently accomplished the nu- 
merical computation of the effect of multiple scattering 
and of the ground reflection in the skylight polarization 
for a special value of the optical thickness r = 0.15, 
corresponding to X = 450 /xfi under normal conditions 
[16]. The reflection on the ground affects the position 
of neutral points very little, in agreement with obser- 
vation (Neuberger [46]). A much larger effect is notice- 
able in the degree of polarization at zenith or at 90° 
from the sun. It is evident from Table III that the 
ground reflection is responsible for the daily variation 
of the maximum polarization, namely for the decrease 
of P with the sun's elevation, in the sense of Fig. 1. 
The theoretical values for P are still much higher than 
the measured ones. 

The observed distances of the neutral points are also 
much higher than the theoretical values obtained by 
Chandrasekhar (for //,, = 0°: .4-point, 19.4° and Ba- 
point, 19.4°; for Ju = 13.9°: ^1-point, 20.9° and 
point, 18.7°). However a remarkable agreement 
found between the theoretical shape of the neutral 
and the shape of neutral lines obser\'ed by Dorno 
Larger scattering particles apparently affect primarily 
the magnitude of the polarization, and the position of 
the neutral points, but have only a slight effect on the 
position of the plane of polarization. This fact is an 
interesting aspect of the physics of scattering by larger 
particles and as such should be studied more exten- 
sively. 

Chandrasekhar's method of exact evaluation of the 
molecular scattering makes possible a quantitative 



Pa- 
was 
lines 
[221. 



86 



METEOROLOGICAL OPTICS 



study of the presence and the nature of larger scatter- 
ing particles. If the exact values of molecular scattering 
are subtracted from the observed values, the remaining 
part is the effect of larger particles, and it is quite evi- 
dent that, for such a purpose, observations should be 
used in which the deviation from the theory is most 
pronounced. This seems to be the case in the dispersion 
of skylight polarization. 

Dispersion of Atmospheric Polarization 

The discussion of polarization in the preceding sec- 
tion refers to "white" light, as it is observed directly 
by the human eye. The measurement of polarization 
in much shorter spectral ranges was started very early 
in skylight investigations. In 1884, Cornu [18] found 
the degree of polarization to be different for different 
colors. During this period of volcanic anomalies the 
polarization at shorter wave lengths was much larger 
than for longer wave lengths. The dispersion of polari- 
zation has been studied since that time by several au- 



liJ 


^:: 

V 


^"^^ 




E 




z "^"^ 




h ^*«lli„ 




^^ 




H 
tn 




• 






ITE 


< 
_j 

■z. 










~~~~- 


< 








V 












X 


•^- 



0.5 0.9 

SOLAR INTENSITY (CAL 



1.3 



CM' 



MIN'') 



Fig. 4. — Distance of the Arago point from the antisolar 
point for /i, = 10.5°, in different colors for different intensities 
of solar radiation {according to Neuberger). 

thors with one result confirmed by all, namelj^ the great 
variability of the dispersion with the turbidity, and 
thus with the weather, location, etc. Since the turbidity 
was not actually measured (except in the latest studies) , 
the different results which have been attained are very 
difficult to compare. If the relativity of the terms 
"pure" and "turbid" atmosphere is admitted, then the 
contradictory results of different authors, even recently 
considered inexplicable [3], can be ordered to show a 
definite trend, confirmed by theoretical considerations. 
For very low turbidity (high altitude) the degree of 
polarization at the point of maximum polarization in- 
creases with the wave length [65]. With increasing tur- 
bidity, the maximum is shifted to the central part of 
the visible spectrum and the difference between polari- 
zation in the red part of the spectrum (Pr) and in the 
blue part (Pb) is decreased (for "pure air" in Gockel's 
definition the difference Pr — Pb becomes smaller than 
the errors of observation). With still larger turbidity 
the maximum is shifted to the blue part, that is, 
Pb > Pr [22, 25, 34, 48, 65].- 



The measurement of distances of neutral points in 
different colors was started by Jensen [1] in 1909. The 
results of his measurements were confirmed by Busch 
[11], who found that the distances of the j4 -point were 
larger the shorter the wave lengths. During the abnor- 
mal period 1912-14, just the opposite was found. This 
result was recently confirmed by Neuberger [45, 46] in 
his measurement of the A-point at hs = 10.5°. Along 
with the A-point distances, the intensity of solar radi- 
ation, the blue color of the sky, etc., were measured 
and the variations of ^4 -point distances with the tur- 
bidity were proved to be as shown in Fig. 4. 

The dispersion of polarization is thus very sensitive 
to the degree of turbidity and could be used as another 
indicator of turbidity. But it can also be used for 
answering the question about the prevailing effect of 
the molecular scattering, or of the presence of larger 
particles in the atmosphere. It is evident that in Ray- 
leigh's theory of primary scattering there is no disper- 
sion, since the degree of polarization P is independent 
of X. If it is assumed with Milch that the light scat- 
tered by large particles is unpolarized, the component 
of the total intensity due to the scattering on large par- 
ticles can be expressed in the form F„ = X^" Nf{<p), 
where a. decreases from 3.5 to 1 with increasing size of 
particles, A'' denotes the number of such particles per 
unit volume, and (p is the scattering angle. It can easily 
be shown [59] that the sign of the difference P(X) — 
P(Xo) is determined by the sign of the expression 

[p/P{\o) - 1](1- X*) + (x^ - x"-*)^„(Xo)//„(Xo), (8) 

where p denotes the degree of polarization in Rayleigh's 
theory of primary scattering, given in equation (1), 
X = Xo/X, and Ig is the total intensity of the component 
due to the primary scattering. If the turbidity is small, 
Fg^O and P(X) > P(Xo) whenever X > Xo. With in- 
creasing turbidity (F„ > 0), the second term in (8), 
having an opposite sign from the first one, reduces the 
difference P(X) — P(Xo) and for a sufficiently large 
turbidity reverses the sign of P(X) — P(Xo). The vari- 
ation of the dispersion with increasing turbidity can 
thus be explained in agreement with observation. But 
the discussion of the distance of the neutral points for 
different wave lengths shows clearly that the assump- 
tion made by Milch, that the light scattered by large 
particles is unpolarized, is not justified. If the light 
scattered by large particles is assumed to be unpolar- 
ized, the distance of neutral points is given by equa- 
tion (4) written in the form 

Pi(Xo) sin- ho = S(\o, ho) — Si{\o, ho), 

and for X 5^ Xo, 

Pi(Xo) sin2 h = x' ['S(Xc, h) - ,Si(Xo, h)]. 

Since Si is actually independent of h, S can be ex- 
pressed by Si and the ratio Si(Xo)/Pi(Xo) can be elim- 
inated from these two equations. The resulting equa- 
tion can be written in the form 

sin^ h — sin^ ha 



1) sin^ ho 



7 sin- ha 



5 + 7 (x* - 1) sin^ ho ' 



(9) 



POLARIZATION OF SKYLIGHT 



87 



Since h < 30°, the numerator and the denominator in 
(9) are always positive, and h > ho whenever Xo > X. 
The distances in blue are larger than in the red part of 
the spectrum, in agreement with the observation made 
for very low turbidity. However, the computed differ- 
ence h — h, for a given ho and given wave lengths 
X, Xo, is about twice as large as observed. What is more 
serious, the great variability of this difference with in- 
creasing turbidity cannot be explained by (9). The ef- 
fect of increasing turbidity can be taken into consid- 
eration only by increasing ho, but the right-hand side 
of (9) increases with ho instead of the observed decrease 
to negative values. This may serve as a proof of the 
incorrectness of the assumption made above. For a com- 
plete discussion it is necessary to include the polarized 
component due to the scattering by large particles also. 
This can be done only by using the Mie-Debye theory, 
as discussed in detail elsewhere [59]. By constructing a 
special model of the distribution, size, and optical prop- 
erties (refractive index) of the large particles, the dis- 
persion of polarization can be computed and compared 
with the observed values through a procedure similar 
to that used in the study of atmospheric haze [28, 51, 
60] and thus a model of the distribution which best fits 
the observations can be found. 

Polarization Anomalies During Twilight 

The same information concerning the size, nature, 
and distribution of scattering particles in the atmos- 
phere can be obtained from any deviations of observed 
values of skylight polarization from those to be ex- 
pected from Rayleigh's theory. Particular emphasis has 
been placed on anomalies during twilight (because of 
the easily determined changes in illiunination along the 
vertical line to the zenith) with the hope that more in- 
formation can be obtained about the vertical distribu- 
tion of scattering particles in this way. But the use of 
twilight anomalies is not as simple as it would seem. 
The first difficulty is the rapid decrease of the intensity 
of skylight, which causes serious difficulties in polari- 
zation measurement. Visual methods quickly become 
uncertain and are very seldom reliable for solar depres- 
sions beyond hs = —5° or —6°. The photographic 
method requires longer exposures during which the 
eventual fluctuations in the degree of polarization and 
in the position of the plane of polarization may cause 
large systematic errors. 

In theoretical investigations the atmosphere can no 
longer be considered as plane-parallel, and refraction 
must be taken into consideration at least to the extent 
of estimating the limit of the earth's shadow. The 
ground reflection, acting for low solar depressions only 
on one side of the horizon, and the different extinction 
values in the solar and antisolar regions make the com- 
putation of the sky polarization rather complicated. 
With respect to the effect of secondary scattering, it is 
valid to offer the same criticism which was presented 
against the use of the zenith intensity for optical sound- 
ing of the upper atmosphere. As Hulburt [27] pointed 
out, the intensity of the secondary scattering increases 
rapidly in comparison with the intensity of primary 



scattering, so that for solar depressions larger than 8°, 
the secondary scattering from the lower level has a 
greater intensity than that of the primary scattering 
from the upper levels still illuminated by direct rays 
from the sun. Hulburt's estimate of this effect was 
based on the measured intensity of skylight near the 
western horizon; the presence of larger particles was 
thus taken into consideration. This may explain the 
much larger values for the ratio of the intensity of the 
secondary and primary scattering {IpHm '■ Isec = 1 : 185, 
hs = -10°9') than computed by Link [39] (/j,™: 
Isec = 2:1) under the assumption of molecular scat- 
tering only. For this reason it is quite difficult to ex- 
plain the high correlation of the polarization anomalies 
(sudden or nonmonotonic decrease of P in the zenith 
for sun's depressions larger than 10°) with the changes 
in the ionization of the E- or F-layer, as observed by 
Khvostikov and a group of Russian scientists. The first 
attempt to explain the anomalies as being associated 
directly with the increase of anisotropy of the ions as 
compared to neutral particles [35, 36, 52] was foimd by 
Ginsburg [23, 24] to be unacceptable because of the 
predominant effect of the secondary scattering. The 
polarization caused only by secondary scattering under 
such conditions was recently estimated by Rosenberg 
[53] as being even larger than observed. The observed 
rotation [49] of the plane of polarization from the direc- 
tion given by the position of the sun cannot be ex- 
plained simply by the asymmetry in the solar illumina- 
tion and should be studied more closely in relation to 
the problem of fluorescent luminescence or other types 
of emission of the night sky. For the study of the emis- 
sion layer the scattering of the emitted light is very 
important and can be used for the determination of the 
height of the emission layer [8]. Since the secondary 
scattered solar radiation may be superimposed upon 
the light from the emission layer, the dispersion of 
polarization of the twilight or night sky could be used 
for separating the phenomena of the lower atmosphere 
from those of the upper levels. Because of experimental 
difficulties there is little hope for the effectiveness of 
this method in the near future. The only possible way 
of separating the intensity of the polarization produced 
in lower levels from the phenomena related to upper 
levels is to compute these quantities using the extinc- 
tion coefficient and other parameters of scattering in 
lower levels, obtained by independent measurements. 
For this purpose the method of an artificial light source 
seems to be quite adaptable. The searchlight beam has 
been used and information about the type and the law 
of scattering has been derived mainly from the total 
intensity measurement [28, 29, 33, 51, 60]. More infor- 
mation can be obtained, however, if the measiurement 
of the polarization is added, as has been done by 
IChvostikov [35]. But since the brightness of the search- 
light beam decreases with the distance from the source, 
the secondary scattering in lower levels should be care- 
fully taken into consideration before any conclusions 
are made about scattering in higher levels. 

The searchlight-beam method definitely offers quite 
new possibilities and if properly used may contribute 



METEOROLOGICAL OPTICS 



largely to the solution of the problem of light scatter- 
ing in the atmosphere. 

Unsolved Problems and Future Research 

As was shown in the preceding sections, much valu- 
able information can be obtained from a comparison of 
measured and theoretical values. Therefore future re- 
search depends primarily upon the development of 
both experimental and theoretical methods. First, there 
is a definite need for better equipment for measuring 
skylight polarization. Such equipment should permit 
objective, fast, and precise measurements of the degree 
of polarization and of the position of the plane of polar- 
ization, in comparatively narrow spectral ranges, in all 
directions over the sky, with special provision for meas- 
urement of weak polarization, thus being adaptable also 
to the measurement of the neutral points. Speed in 
measurement is required not only for almost simultane- 
ous measurements at different wave lengths and at dif- 
ferent places in the sky, but mainly for the possibility 
of recording the shorter fluctuations observed in the 
degree of polarization [57] as well as in the position of 
neutral points [45, 46]. These fluctuations, not observ- 
able by the older methods or eliminated by improper 
smoothing, seem to precede cloud formation in a clear 
sky, and might be used in the study of condensation 
processes in incipient clouds. With sensitive photomul- 
tipliers and with a proper amplification, the sensitivity 
of measurement can be increased beyond that of the 
human eye, and observations can be extended far into 
the twilight or used for optical sounding by searchlight 
beams. 

From the theoretical standpoint, Chandrasekhar's 
computations can easily be completed, and skylight 
polarization due to multiple molecular scattering can 
be computed, in all directions and for all wave lengths, 
for larger solar elevations when the atmosphere can be 
considered as plane-parallel. But the greatest advantage 
of this method is that it can be extended in such a way 
that almost all currently unsolved problems of atmos- 
pheric polarization can be solved. In the case of reflec- 
tion at the ground, if, for example, the polarization 
according to Fresnel's law were taken into considera- 
tion as observed in the vicinity of large water surfaces 
[26], the anomalies mentioned earlier could be explained 
theoretically. If the Mie-Debye theory of large-particle 
scattering could be simplified in such a way that the 
corresponding scattering matrices could be computed 
without essential difficulties, the effect of large particles 
could also be taken into consideration. So far Chan- 
drasekhar's theory has been limited to a plane-parallel 
atmosphere, and twilight anomalies have been unac- 
cessible to theoretical investigation of similar type. 
Chandrasekhar [14, 15] already has shown the way to 
extend the theory for a spherical atmosphere. It is nec- 
essary only to work out the suggested method in more 
detail. The exact theory of twilight phenomena cannot, 
however, be developed without the consideration of re- 
fraction and the corresponding bending of light paths 
in the atmosphere. This part of the problem does not 
represent any special difficulty since complete refrac- 



tion tables, with all the parameters necessary for such 
a computation, are now available and can be con- 
veniently used for this purpose [40]. 

Hence, many problems quite accessible by modern 
facilities are open to further investigations. In the re- 
view given above, the list of problems to be solved is 
not exhaustive; new problems may easily arise as the 
study of skylight polarization progresses further. For 
this reason atmospheric polarization deserves more 
attention than it has received up to now. 

REFERENCES 

A detailed discussion of problems of skylight polarization 
will be found in references [1] through [5]. Reference [6] gives a 
detailed description of instruments used in polarization meas- 
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1. BuscH, F., und Jensen, C, "Tatsachen und Theorien der 

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POLARIZATION OF SKYLIGHT 



89 



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wird." Ann. Phys., Lpz., 59:493-537 (1919). 

56. "Neue theoretische Untersuchungen iiber die Polari- 
sation des Lichtes an triiben Medien und deren Konse- 
quenzen fiir die Probleme der atmospharischen Polarisa- 
tion." Meteor. Z., 37:12-22 (1920). 

57. Sekera, Z., "Lichtelektrische Registrierung der Him- 

melspolarisation." Beitr. Geophys., 44:157-175 (1935). 

— "tJber die Vergleichsmoglichkeit der visuellen und 
lichtelektrischen Messung der Himmelspohirisation." 
(?os. Pest. Math., 67:278-287 (1938). 

— "Dispersion of the Atmospheric Polarization in Rela- 
tion to the Size and Nature of Larger Scattering Par- 
ticles." (Prepared for publication.) 

60. Siedentopf, H., "Zur Optik des atmospharischen Dunstes." 

Z. Meteor., 1:417-422 (1947). 

61. Smosarski, W., "Zur Theorie des Cornu-Photopuhirime- 

ters." Beitr. Geophys., 54:235-244 (1939). 

62. "Polarisation des Himmelslichtes im Weltpol und 

andere Beobachtungen." Beitr. Geophys., 48:213-224 
(1936). 

63. SoRET, J. L., "Influence des surfaces d'eau sur la polarisa- 

tion atmospherique et observation de deux points neu- 
tres a, droite et il gauche du Soleil." C. R. Acad. Sci., 
Paris., 107:867-870 (1888). 

64. "Sur la polarisation atmospherique." Arch. Sci. 

phys. nat., 20:429-471 (1888). 



58. 



59. 



90 METEOROLOGICAL OPTICS 

65. TicHANOwsKi, J. J., "Resultate der Messungen der Him- 68. van de Hulst, H. C, "Scattering in the Atmospheres of 

melspolarisation in verschiedenen Spektrumabschnit- the Earth and the Planets" in The Atmospheres oj the 

ten." Meteor. Z., 43:288-292 (1926). Earth and Planets, G. P. Kuipee, ed. Chicago, Univer- 

66. "Die Bestimmung des optischen Anisotropiekoeffi- sity of Chicago Press, 1949. (See pp. 49-112) 

zienten der Luftmolekulen durch Messungen der Him- 69. Voss, W., "Eine Abart des Savartschen Polariskops." 

melspolarisation." Phys. Z., 28:252-260 (1927). Z. InstrumKde., 52:332-333 (1932). 

67. TousEY, R., and Hulburt, E. O., "Brightness and Polar- 70. Worner, H., "Messungen der Sonnenstrahlung, der Him- 

ization of the Daylight Sky at Various Altitudes above melspolarisation und der Blaufiirbung des Him- 

Sea Level." J. opt. Soc. Amer., 37:78-92 (1947). melslichtes." Z. Meteor., 3:166-169 (1949). 



VISIBILITY IN METEOROLOGY 

By W. E. KNOWLES MIDDLETON 
National Research Council, Canada 



Introduction 

This discussion will be devoted to a brief study of 
those interrelations between the optical properties of 
the atmosphere and the characteristics of human vision 
which determine how far a given object can be seen at 
such and such a moment. This important distance, 
when referred to the ordinary objects which lie around 
the horizon of a meteorological observer, is called by 
meteorologists "the visibility"; it is not with any hope 
of changing this terminology, but only in the interests 
of logical discussion, that the same quantity, applied 
now to any object, will here be given the name visual 
range. The term is self-explanatory. 

The theory of the visual range is by this time in a 
fairly satisfactory condition, largely because of very 
extensive researches conducted during World War 
II, especially in the United States. As in many other 
divisions of meteorology, however, the extreme com- 
plexity of atmospheric conditions makes it difficult to 
apply the available theory to actual instances, especially 
in the important case of visual range along inclined 
paths. Even the instrumentation necessary to measure 
the appropriate optical constants of the atmosphere has 
not been developed to the point where it is in general 
use at meteorological stations. Theory is well in front 
of practice. 

We are unable to refer the reader to any very up-to- 
date summaries of the whole field; in fact to nothing 
later than 1941 [33, 35]. In view of our restrictions on 
space we must assume that at least one of these two 
monographs is available to the reader. It is to be hoped 
that before very long a more up-to-date general account 
will be published. 

The Behavior of Light in the Atmosphere 

Light, by its interaction with the atmosphere, pro- 
duces many beautiful phenomena which are dealt with 
elsewhere in this book. Our concern here is only with 
the way in which it is attenuated in its passage through 
the air and with the manner in which it is diffused by 
scattering. 

As far as any practical interest is concerned, we may 
neglect those rare occasions when the air is nearly free 
from particles larger than the molecules of gases, in 
view of the fact that the visual range in such a pure 
atmosphere would be several hundred kilometers at sea 
level. The reader may be referred to Cabannes [10] for 
a masterly discussion of such molecular scattering. On 
all occasions when the visual range is of any practical 
importance, by far the greater part of the effect of the 
atmosphere on light is produced by particles much 
larger than molecules, which may be thought of as the 
disperse phase of an atmospheric colloid or aerosol. 



These particles are of many kinds, but from our 
standpoint the most interesting of them are the liquid 
droplets, generally aqueous solutions of hygroscopic 
substances, which in various radii from about 10~^ to 
10~^ cm form the obscuring matter in haze, fog, and 
mist. The actual nature of the hygroscopic nuclei in- 
volved is one of the great unsolved problems of meteorol- 
ogy, and has become the subject of a controversy, for 
the details of which the reader should consult Wright 
[52, 53, 54, 55, 56], Simpson [43, 44] and Findeisen 
[21]. Whatever their nature, they increase in size with 
increasing relative humidity, as more and more water 
condenses on them. Up to a radius of about 0.5 micron 
(5 X 10"^ cm) they show selective scattering in visible 
light which makes them appear bluish by reflection, 
and we call them haze. With further increase in size, 
this selectivity practically disappears, and we have 
fog, which is typically colorless. We must now consider 
in a little more detail the scattering of light by such 
spherical particles. 

For particles of radius a in the range O.IX < a < 
lOX (X = wave length of light), which includes most 
kinds of haze and some fogs, the theory of Mie [38]^ has 
been found entirely adequate. Starting with the electro- 
magnetic theory, Mie was able to calculate the intensity 
/ (lumens per steradian per particle per lumen per m^ 
illuminance) in a direction making an angle 4) with that 
of the incident light. This is a function of 27ra/X and of 
m, the index of refraction of the particles (1.33 for 
water). To show the large variation of the polar diagram 
of the scattered light with the radius of the particle. 
Fig. 1 is presented, the limiting value as a -^ being 
shown by a dotted curve (Rayleigh atmosphere). 

By integrating I{4>) over the sphere, the total amount 
of light scattered may be calculated, and it is found that 
this is generally greater than that incident on the 
droplet. For large droplets the ratio K of these quantities 
approaches 2, and the explanation is to be found in 
diffraction. Since K has been calculated [30, 47] as a 
function of the parameter 2xa/X, the coefficient of 
attenuation by scattering for an atmosphere containing 
N droplets per m', each of radius a, is 



b = NKto^ meter 



(1) 



In such droplets, as has been shown by Zanotelli [57], 
absorption is negligible, so that the extinction coefficient 
cr is also given by equation (1). 

The correctness of these ideas is now acknowledged, 
and they have been remarkably well verified in natural 
haze by Dessens [15, 16], who caught haze particles on 
minute spiders' webs. 

For the larger droplets of fog, Bricard [8, 9] has 

1. Concisely set forth by Stratton [46, p. 563]. 



91 



92 



METEOROLOGICAL OPTICS 



produced an adequate geometrical theory of scattering, 
serving as an extrapolation of the Mie theory. Many 
workers, notably Houghton and Radford [26] and Bri- 
card [6, 7], have measured the size distribution in 
natural fogs, obtaining unimodal curves with maxima 
in the region between 4 and 10 microns radius. Such 
fogs should be nearly nonselective. All these researches 
may be criticised on the basis of sampling, especially 
since Driving and his co-workers [18] have presented 
indirect evidence for the presence of large numbers of 
very small droplets. Such evidence is hard to obtain 
because, as Dessens [15] points out, the total optical 
effect of these small particles is not very important. 

The researches of Dessens should be repeated and an 
attempt made to extend them to natural fogs in order 
to decide this point. It is also possible that the use of 
the electron microscope in such work might settle the 
controversy about the nature of the nuclei. Another 
line of research which might be undertaken in some 
sparsely inhabited region concerns the explanation of 



^'^"^ 90° 








y^ 






3.0 \ 




/ 


4S«< 


^""^ ^\ 






/ j^i^^^y 


'^>^ 


$:>. V\ 






/ '^yl\ 




N;^N ^ 


\~"~~\ 


\ 


1 ,#^J 




\-^° 


\ 


^\6,0 


-O.O/.'l J / 




\'^'\ 


\ 


\ ^ 


ill f / 




: 1 




1 


\ \ \ V 




-1 Oil 

/ /// 


+ 1 


l+E 


\'W" 


^_y 




/ 




\ '^t-iL /^ 




^■y ^ 




1 


\ "^^^J^kJ 


^^ 


<_^ 







0° 



Fig. 1. — Polar diagram of scattering by water droplets, nor- 
malized at 90°. The radii are in log units. The numbers on the 
curves refer to values of 2iral\. 



the surprisingly low selectivity shown by very clear 
air such as occasionally permits a visual range of 150 
or 200 km. Observations, chiefly in Europe, never 
seem to show anything like the inverse fourth power 
of the wave length demanded by the theory for pure 
gases. As a hypothesis, one may assume the effect of a 
comparatively small number of relatively large particles. 

The Reduction of Contrast by the Atmosphere 

The common observation that the more distant an 
object, seen in daylight, the greater its luminance, was 
first reduced to mathematical form in 1924 by Kosch- 
mieder [29]. The simplest case is that of a black object 
of intrinsic luminance zero seen against a horizon sky 
of luminance 5^. On the assumption of a uniform 
atmosphere having a scattering coefficient &o, and illu- 
mination by the sun and a uniform (overcast or cloud- 
less) sky, Koschmieder , showed that such an object 
seen at a distance r will have an apparent luminance 



He further showed that an object which is not black, 
but has an intrinsic luminance Bo, will at a distance r 
have an apparent luminance 



B = 5oe-'«' + B,(l 



i^r\ 



(3) 



We cannot calculate 5o without knowledge of the 
distribution of light, even if we know the properties of 
the object. 

In these equations no mention is made of absorption, 
and while it is customary to write similar equations 
using (7 instead of 6, it is not immediately obvious how 
such an extension can be justified. Actually a more 
detailed analysis, using the concept of the space light 
Ba, which is a function of the scattering properties of 
the air and of its illumination, does lead to an equation 



B 



Boe'""^ + Bu{\ - e-'n- 



(4) 



Such an analysis has been carried out by Duntley 
[19], who also threw off the restriction of horizontal 
vi^on and introduced a quantity R which he called the 
optical slant range, which "represents the horizontal 
distance in a homogeneous atmosphere for which the 
attenuation is the same as that actually encountered 
along the true path of length R" [19, p. 182]. The 
equation for downward oblique vision becomes 



B 



BM 



<^o 



(1 - e""'^) + B, e-'"'', 



(5) 



in which Ba{0) and o-q are the values of Ba and er cor- 
responding to the air near the ground. In the horizontal 
case it turns out that Bf, is to be identified with Ba{0)/(ro. 
A more useful statement of the law may be made in 
terms of contrast. li Ba and Bd are the inherent lumi- 
nances of two objects adjacent in the field of view and 
-Bffi and B,^ their apparent luminances, then defining 
contrast in the usual way, 



Co 



Bo — Bo 



Cu = 



Br — Br 



(6) 



Bi = B,.(l - e-'»0. 



(2) 



we may write two equations such as (5) and simplify 
to obtain I 

Cr = CoiBo/B'R)e-''^ . (7) 

This is completely general. If we confine ourselves to 
objects seen against the horizon sky, B'{= B,,) is inde- i 
pendent of distance, and (7) reduces to ^ 

Cr = Coe-"\ (8) 

We have not space to expound the theory further in its 
applications to oblique vision, but it should perhaps be 
pointed out that practical situations generally require 
information which, at best, has to be estimated. 

Equation (8) has been tested more or less thoroughly 
by many workers, and there is no longer any doubt 
about its adequacy. A matter about which there is some 
disagreement, however, is the exact nature of the extinc- 
tion coefficient a. In deriving equations similar to (5), 
Duntley [19] has made use of a theory originally de- 
veloped by Schuster [41] which dealt with the distribu- 
tion of diffuse radiation in stellar atmospheres. The 



VISIBILITY IN METEOROLOGY 



93 



extinction coefficient used, which was introduced by 
Duntley, is that pertaining to diffused radiation. The 
pi'esent writer beheves that this is incorrect. The only 
portion of the hght from an object which goes to form 
an image of it is that which reaches the eye from the 
direction of the object and it would seem logical to use 
the extinction coefficient for directed light in such a 
discussion. It seems probable that the choice of the other 
quantity was conditioned bj' a desire to explain some 
results of Douglas and Young [17] which suggested that 
the value of u determined by the photometry of a 
projector is slightly less than that calculated from 
(8). The author has recently shown [37] that the dis- 
crepancy may arise from other causes. It would never- 
theless be a comfort to have a long series of simultaneous 
measurements of <j by the two methods, especially in 
fog. 

The Relevant Properties of the Eye 

If we are to use equations such as (7) to determine 
the visual range of objects, it is obvious that we need to 
know the least value of contrast that the eye can 
appreciate. Similarly, if we are interested in the visual 
range of light signals, we need data on the threshold 
illuminance Et at the eye. This can easily be trans- 
formed into a contrast limen, so that one set of data is 
really sufficient for both problems. 

The eye can exist in two states of adaptation, known 
as the dark-adapted and light-adapted conditions, the 
transition taking place at a field luminance of about 
2 X 10~^ candles m~^. The reader may be referred to 
Stiles, Bennett, and Green [45] for a discussion of the 
properties of the eye in the two states and we shall only 
note here that color vision is restricted to the light- 
adapted state. 

It has been known for a long time that the threshold 
of contrast increases at low \'alues of luminance and for 
objects of small angular subtense. In meteorology it has 
become a sort of convention to adopt a value e = 
±0.02 for ordinary objects in the daytime; but there 
is no doubt that this is frequently far from the truth. 
During World War II a very extensive investigation was 
made at the Louis Comfort Tiffany Foundation, and re- 
ported by Black well [4]. This report covers 450,000 
observations of circular objects ranging from 0.6 to 360 
minutes of arc in angular diameter, and over a very wide 
range of background luminance (5 X 10^'' to 4 X 10- 
candles m"^) ; Fig. 2 shows one set of curves interpolated 
from some of the results. Note the straight portions of 
the curves; over this range of visual angle the product 
of the area and the luminance of a stimulus {i.e., its 
candlepower) is a constant; this is the range in which 
the signal can be considered a "point source," and 
values of threshold illuminance may easily be derived 
from the ciu'ves. 

These curves refer to the contrast required for 50 
per cent probability of detection by an observer using 
both eyes under natural conditions. For almost certain 
detection the values of contrast should be multiplied 
by 2 or at mo.st by 3. 

A recent field investigation by Blackwell [5] makes 



it highly probable that these laboratory values will 
also apply under field conditions, provided that the 
factors of attention and search do not enter. Other 
experiments [2, 11] indicate that vision through binocu- 
lars follows the same laws, provided that allowance is 
made for the reduction of contrast by the optical 
system. 

The factors of attention and search remain to be 
investigated, as does the enormously complicated phe- 
nomenon of recognition, which also brings in the question 
of visual acuity, and is a matter worthy of the interest 
of any number of extremely able psychologists. 

There have been many investigations of the threshold 
illuminance of lights and its dependence on field lumi- 
nance (see [45]). While satisfactory absolute values can 
be derived from the Tiffany data, "practical" values 
have been sought, with the general result of about 0.2 
lumens km~' for fixed, achromatic sources on a moonless 
night. If the light is flashing, a somewhat greater 
illuminance is required for equal conspicuity, depending 




Fig. 2. — Threshold of contrast of circular objects, from the ■ 
Tiffany data. Each curve refers to the background luminance 
marked. 



on the time of the flash; this has been investigated by 
various authors (see [45]). Threshold illuminance varies 
with the color of the point source, and there are some 
papers [24, 25, 34] dealing with the i-ecognition of 
colored lights. The general result of these investigations 
is to show that only red and blue-green are "safe" colors 
near their threshold illuminance. 

The Calculation of the Visual Range 

We are now in a position to combine the results of 
the last three sections and calculate the visual range 
of objects or of lights. For either computation we must 
know the extinction coefficient o-, and in the case of an 
inclined path of sight we must also know or estimate its 
variation in the vertical. We must know the contrast 
threshold appropriate to the angular size (and probably 
the shape) of the object and to the field luminance; or 
the threshold illuminance for a light of the charac- 
teristics concerned, against the existing background. 
There is really no fundamental difference between the 



94 



METEOROLOGICAL OPTICS 



two cases, but it is simpler not to think of contrast when 
dealing with a point source of light. 

Dealing first with the visual range of an object seen 
against the horizon sky, the problem is simply to put 
the proper values of Co and e in equation (8) and solve 
for r. For a given object, which looks smaller as it 
becomes more distant, t is unfortunately an empirical 
function of r. 

The standard procedure, used by all writers until 
very recently, is to restrict the problem to "large" 
objects in full daylight; that is, to the approximately 
vertical portions of the curves at the extreme left of 
Fig. 2, so that e may be considered constant. Meteoro- 
logical writers have adopted a quantity variously called 
the standard visibility [53], Luftlichtweite [32] and, more 
recently, the meteorological range [20], calculated on the 
assumption that e = ±0.02. Let us call this Vm, and 
note that if it is referred to a black object (Co = —1) 
against the horizon sky, it is just a convenient sub- 
stitute for (70 ; because if we write (8) 



-0.02 = -e-""''"' 
and take natural logarithms, we obtain 

Vn, = 3.912/0-0 . 



(9) 



(10) 



The "meteorological range" is defined as "that distance 
for Avhich the contrast transmittance of the atmosphere 
is two per cent" [20, p. 238]. 

If now we break away from the restrictions of a 
"large object" and full daylight, we immediately run 
into the difficulty that equation (8) can be solved only 
by a process of successive approximations. The awk- 
wardness of this led the workers at the Tiffany Founda- 
tion to devise a remarkable series of nomograms [20], 
prepared for various levels of field luminance from over- 
cast starlight to full daylight, from which the visual 
range of an object of any area may be read directly if 
its inherent contrast and the meteorological range are 
known. These nomograms were based on the actual 
Tiffany data referred to previously, and therefore cor- 
respond to a 50 per cent probability of detection. It 
is hoped that further nomograms will be forthcoming, 
based on a probability of detection much nearer unity, 
though the existing ones may be used for many purposes 
by dividing the inherent contrast of the object by 2 
before entering the nomogram [20, p. 249]. 

The estimation of the inherent contrast of the object 
remains a stumbling block, except for the ideal black 
object. If we had a grey object of luminance factor 
13 standing vertically under a sky of uniform luminance 
Bh, its inherent luminance would be Bo = Bhl3/2 and 
its contrast Co = |S/2 — 1. A white object, for example, 
would have a contrast of — 3^, and this quantity has 
been used in a great deal of theory under the mistaken 
assumption that a densely overcast sky is uniform. 
Unfortunately its luminance is about three times as 
great at the zenith as at the horizon [39] and it has been 
shown [36] that, for a vertical white object, this results 
in values of Co between and +1, depending on the 
reflectance of the ground. The complications naturally 
increase when the sun is shining. 



Turning now to oblique paths of sight, we have the 
remarkably ingenious theory of Duntley [19] and the 
nomograms based on it [20]. The reader is asked to 
consult the two papers concerned, especially the first, 
which is far too long to summarize here, and to make up 
his own mind as to the practical utility of the theory. 
It may be that some "operational" research is indi- 
cated. 

The visual range of lights at night presents a simpler 
problem. The illuminance from a source of / candle- 
power at a distance r in an atmosphere of extinction 
coefficient o-o is | 



Er = /r~'e~"°^ 



(11) 



and the visual range is then given by introducing the 
threshold illuminance Eti 



E, = ir 



-'e-"'\ 



(12) 



A suitable nomogram may easily be constructed for 
the solution of (12). If oblique vision is involved, the 
problem of measuring or estimating a remains. 

Instruments for the Measurement of the Visual Range 

Before we can calculate the visual range of any 
particular object or light signal, we must have a knowl- 
edge of a or of Fm. A large number of different instru- 
ments have been designed for the measurement of these 
quantities, some requiring photometric settings on the 
part of the observer, others completely objective or even 
automatic, but none of them seem to be in use at any 
considerable number of meteorological stations. 

Nearly all these instruments fall into four classes: 
(1) devices which measure the ti-ansmittance of a 
more-or-less extended sample of the atmosphere; (2) 
instruments which measure the reduction of known 
contrasts; (3) instruments which measure the light 
scattered from a small sample of air at one or many 
angles ; and (4) empirical meters of various types which j 
do not measure a directly. I 

Transmittance meters form a fairly numerous class, 
which may be divided into two subclasses depending 
on whether they are usable only at night or at all 
times. Those for use only at night are generally visual 
telephotometers and may make use of a distant light, 
as for instance that of Collier and Taylor [13], or of a 
beam of light projected from the instrument and re- 
turned by a distant mirror, as that of Foitzik [22, 23]. 
For a very excellent discussion of visual telephotom- 
eters and their limitations the reader may be referred 
to a paper by Collier [12]. 

A similar duality of optical systems is found in 
photoelectric transmittance meters, which are often 
usable throughout the day and night. Those with a 
distant mirror, represented by that of Bergmann [3], 
can easily make use of a modulated light beam and a 
tuned amplifier to make them insensitive to daylight, 
and a null method of measurement to reduce the effect 
of fluctuations in the supply voltage. They have the 
disadvantage of complexity and very high cost. Simple 
photometry of a distant projector [17] is cheaper. 



VISIBILITY IN METEOROLOGY 



95 



All telephotometers suffer from a serious contraction 
of their scales as the visual range becomes greater. It 
has also been shown by Middleton [37] that the beam 
must be made extremely narrow if very large errors are 
to be avoided in some kinds of weather. 

Telephotometers have been devised which measure 
the ratio of the luminances of a distant object and the 
horizon sky just above it, as for example that of Lohle 
[31]. Difficulties of eliminating stray light, at least in 
any simple routine of observation, limit the precision 
of such instruments. Somewhat more practical, particu- 
larly with modern photoelectric circuits, is the measure- 
ment of the apparent luminance of a nearby deep black 
box, specially constructed for the purpose. 

Scattering meters are not numerous. The "polar 
nephelometer" of Waldram [48, 49] -which measures the 
light scattered by a sample of air in almost any direc- 
tion is an excellent example. The "Loofah" [1] measures 
the scattering at 150°, which has been found to approxi- 
mate a mean value under many conditions, especially 
at sea. All such meters fail under urban conditions 
because they take no account of absorption. 

Finally there are any number of empirical instruments 
(Jones [28], Wigand [51] and others) which operate 
by the addition of "veiling glare" to the distant scene. 
Of these, the type most sound in theory was devised 
independently by Shallenberger and Little [42] in the 
United States, and by Waldram [50] in England. It is 
called the "disappearance range gauge" by Waldram, 
and presents the observer with two images of the hori- 
zon one above the other, of which the fainter may be 
made to disappear by turning a control. It is at least 
a valuable aid to visual estimation. 

In spite of the very large number of instruments which 
have been devised, the problem remains open for solu- 
tion; and perhaps it is largely an economic problem. 
The writer hesitates to predict the advent of a useful 
instrument at such a cost that meteorological services 
will give it wide distribution. 

The Visual Range in Practice 

In the absence of instruments, meteorological ob- 
servers estimate "the visibility" by observing whatever 
objects (or lights at night) maybe available around their 
stations. It is officially recommended [27] that dark- 
colored marks should be used in the daytime, and that 
they should be visible against the horizon sky whenever 
possible ; also that they should be of reasonable angular 
dimensions. The Conference of Directors at Washington 
in 1947 also recommended a table [27, p. 118] which 
relates the visibility of lights to the daytime visibility 
code. This table was prepared on the basis of equations 
(10) and (12), using three different and highly arbitrary 
values of Et , "pending the results of further investiga- 
tion." We shall return to this matter in a moment, but 
first we wish to refer to resolution 169 of the same con- 
ference [27, p. 220], which sets forth the "Table for 
VV (Visibility)." This table proceeds in steps of 20 
meters from 20 to 200 m, which is probably useful; but 
then it continues in steps of 200 m up to 16 km! It is 



unfortunate that the framers of the code omitted to 
provide instructions which would tell the unhappy 
observer how he is to distinguish between a visibility 
of 15.6 km and one of 15.8 km. Among the workers in 
this field it would be difficult to find one optimist who 
would expect even the most elaborate instrument to 
perform such a task. 

In the absence of absurd requirements such as the 
above, the estimation of "visibility" in the daytime is a 
fairly satisfactory procedure if a reasonable series of 
suitable marks is available — not necessarily one for 
every distance in the code. It is otherwise at night. 
The central difficulty of night observations lies in the 
unknown and variable adaptation level of the observer's 
eye, accentuated by the fact that the observer has 
recently come from a brightly lighted room. In the 
absence of an instrument the observation is often the 
merest guess, and a suitable objective meter is greatly 
to be desired for use at night. 

We shall close with a brief remark on the treatment 
of visibility observations as climatological data. The 
usual procedure is to count the number of occurrences of 
each code number, but it has been pointed out by 
Poulter [40] and by Wright [53] that this gives an 
undue prominence to the greater visual ranges. The 
expedients adopted by these two workers to improve 
the situation are very different. Poulter multiplied each 
frequency by the reciprocal of the range of distances 
embraced by the corresponding code number; Wright 
calculated what amounts to the mean extinction coeffi- 
cient. Neither of these procedures involves much extra 
work and they should be given consideration by the 
climatologists. 

Possibilities for Progress 

It will be evident from what has been set down above 
that any further progress is likely to be made in the 
direction of experiment rather than theory. Our most 
hampering uncertainty concerns the value, or range of 
values, of the threshold of contrast actually entering 
into meteorological observations of "visibility," and 
some serious effort should be made to clear this mat- 
ter up. The questions of attention and search are also 
in this domain of psychophysics, and could be the 
subjects of an immense amount of work. However, they 
are of military rather than meteorological interest. 

On the physical side, the elegant researches of Des- 
sens should be extended, and the question of the origin 
of the nuclei needs further expert attention. 

There is also a need for new instruments: a simple, 
inexpensive one for use at many stations mainly, or 
even exclusively, at night; and a more elaborate tele- 
photometer or other such "visibility meter" for impor- 
tant stations like aircraft carriers and large airports. 
In order to be of any use at all, an instrument of the 
latter sort would have to be very accurate, sensitive, 
and stable. 

Finally, the applause of all meteorologists and avia- 
tors is certain to greet anyone who devises a really 
practical method of measuring the transparency of the 
atmosphere as a function of height for at least a few 



96 



METEOROLOGICAL OPTICS 



thousand feet above the ground. This is certainly our 
fading practical problem in this subject. 

REFERENCES 

L Admiralty Rbseahch Laboratory, A Hazemeter for Di- 
rect Measureynent of Atmospheric Scattering Coefficient. 
A.R.L. Report A.R.L./R 1/K.904, London, March 1949. 

2. Bartley, S. H., and Chute, Eloisb, Final Re-port on the 

Effects of Binocular Magnification on the Visibility of 
Targets at Low Levels of Illumination. O.S.R.D. Rep. 
No. 4433, Nov. 30, 1944. 

3. Bergmann, L., "Ein objektiver Sichtmesser." Phys. Z., 

35:177-179 (1934). 

4. Blackwell, H. R., "Contrast Thresholds of the Human 

Eye." /. opt. Soc. Amer., 36:624-643 (1946). 

5. Report of Progress of the Roscommon Visibility Tests, 

June 1947-Dec. 1948. Paper read to the Aviation Light- 
ing Comm. of the I.E.S., Washington, Apr. 21, 1949. 

6. Bricard, J , "fitude de la constitution des nuages au 

sommet du Puy-de-D6me." La Meteor., ser. 3, pp. 83-92 
(1939). 

7. "Contribution a I'^tude des brouillards naturels." 

Ann. Phys., Paris, ser. 11, 14:148-236 (1940). 

8. "Lumiere difTus^e en avant par une goutte d'eau 

sph^rique " /. Phys. Radium, ser. 8, 4:57-66 (1943). 

9. "Reflexion, refraction et diffraction de la lumiere 

par une goutte d'eau sph^rique." Ann. Geophys., 2:231- 
248 (1946). 

10. Cabannes, J., La diffusion moleculaire de la lumiire. (Avec 

la collaboration de Yves Rocard.) Paris, Les Presses 
Universitaires de France, 1929. 

11. Coleman, H. S., and Verplanck, W. S., "A Comparison 

of Computed and E.xperimental Detection Ranges of 
Objects Viewed with Telescopic Systems from Aboard 
Ship." J. opt. Soc. Amer., 38:250-253 (1948). 

12. CoLLiEEj L. J., 'Visual Telephotometry." Trans. Ilium. 

Engng. Soc. London, 3:141-154 (1938). 

13. and Taylor, W. G. A., "A Telephotometer Employing 

the Maxwellian View Principle and Its Use in Measuring 
Atmospheric Transmission." /. sci. Instrum., 15:5-17 
(1938). 

14. Dessens, H., "Les noyaux de condensation de I'at- 

mosphere." La MHeor., ser. 4, No. 8, pp. 321-327 (1947). 

15. "Brume et noyaux de condensation." Ann. Geo- 
phys., 3:68-86 (1947). 

16. "Un compteur de particules atmospheriques." La 

Meteor., ser. 4, No. 8, pp. 328-340 (1947). 

17. Douglas, C. A., and Young, L. L., Development of a Trans- 

missomeler for Determining Visual Range. U. S. Dept. of 
Commerce, C.A.A. Tech. Div. Rep. No. 47, Feb. 1945. 

18. Driving, A. J., Mironov, A. V., Morozov, V. M., and 

Khvostikov, I. A., "The Study of Optical and Physical 
Properties of Natural Fogs." Izvesiiia Akad. Nauk 
(SSSR), Ser. Geogr. i Geofiz., No. 2, pp. 70-82 (1943) 
(in Russian). 

19. DuNTLEY, S. Q., "The Reduction of Apparent Contrast by 

the Atmosphere." J. opt. Soc. Amer., 38:179-191 (1948). 

20. "The Visibility of Distant Objects." /. opt. Soc. 

Amer., 38:237-249 (1948). 

21. FiNDEiSEN, W., "Entstehen die Kondensationskerne an 

der Meeresoberflache?" Meteor. Z., 54:377-379 (1937). 

22. FoiTZiK, L., "Ein neuer Sichtmesser." Meteor. Z., 50:473- 

474 (1933). 

23. "tjber ein Gerat und eine Methode zur Messung der 

Tages- und Nachtsicht (Sichtmesser)." Z. Meteor., 1 :330- 
337 (1947). 



27 



28 



32 



33 



24. Hill, N. E. G., "The Recognition of Coloured Light Sig- 

nals Which Are Near the Limit of Visibility." Proc. 
phys. Soc. Lond., 59:560-574 (1947). 

25. Holmes, J. G., "The Recognition of Coloured Light Sig- 

nals." Trans. Ilium. Engng. Soc. London, 6:71-97 (1941). 

26. Houghton, H. G., and Radford, W. H., "On the Measure- 

ment of Drop Size and Liquid Water Content in Fogs 
and Clouds." Pap. phys. Ocean. Meteor. Mass. Inst. 
Tech. Woods Hole ocean. Instn., Vol. 6, No. 4 (1938). 

International Meteorological Organization, Con- 
ference OF Directors, Washington, 1947, List of 
Resolutions. Lausanne, O.M.I. , 1948. 

Jones, L. A., "A Method and Instrument for the Measure- 
ment of the Visibility of Objects." Phil. Mag., Ser. 6, 
39:96-134 (1920). 

29. KoscHMiEDER, H., "Theorie der horizontalen Sichtweite." 

Beitr. Phys. frei. Atmos., 12:33-55 and 171-181 (1924). 

30. La Mer, V. K., and Sinclair, D., Verification of Mie 

Theory. O.S.R.D. No. 1857. Dept. of Commerce Office of 
Publication Board, Rep. No. 944. 

31. LoHLE, F., "tJber ein Sichtphotometer zur Messung der 

optischen Triibung der bodennahen Luftschicht." Z. 
tech. Phys., 16:73-76 (1935). 

"Sichtschatzung und Luftlichtmessung." Z. angew. 

Meteor., 53:71-82 (1936). 

Sichibeohachtungen vom meteorologischen Standpunkt. 

Berlin, J. Springer, 1941. 

34. McNiCHOLAS, H. J., "Selection of Colors for Signal 

Lights." /. Res. nat. Bur. Stand., 17:955-980 (1936). 

35. MiDDLETON, W. E. K., Visibility in Meteorology, 2nd ed. 

Toronto, Univ. of Toronto Press, 1941. 

36. "Note on the Visual Range of White and Grey Ob- 
jects." Quart. J. R. meteor. Soc, 73:456-459 (1947). 

37. "The Effect of the Angular Aperture of a Telepho- 
tometer on the Telephotometry of CoUimated and Non- 
collimated Beams." J. opt. Soc. Amer., 39:576-581 (1949). 

38. Mie, G., "Beitrage zur Optik truber Medien, speziell 

kolloidaler Metallosungen." Ann. Phys., Lpz., 25:377- 
445 (1908). 

39. Moon, P., and Spencer, D. E., "Illumination from a Non- 

uniform Sky." Ilium. Engr. N.Y., 37:707-726 (1942). 

Poulter, R. M., "The Presentation of Visibility Observa- 
tions." Quart. J. R. meteor. Soc, 63:31-45 (1937). 

Schuster, A., "Radiation Through a Foggy Atmosphere." 
Astrophys. J., 21:1-22 (1905). 

Shallenberger, G. D., and Little, E. M., "Visibility 
Through Haze and Smoke and a Visibility Meter." 
/. opt. Soc Amer., 30:168-176 (1940). 

Simpson, G. C, "Sea-Salt and Condensation Nuclei." 
Quart. J. R. meteor. Soc, 65:553-554 (1939). 

"Sea-Salt and Condensation Nuclei." Quart. J. R. 

meteor. Soc, 67:163-169 (1941). 

Stiles, W. S., Bennett, M. G., and Green, H. N., Visi- 
bility of Light Signals with Special Reference to Aviation 
Lights. Aer. Res. Comm. Reports and Mem., No. 1793, 
London, 1937. 

Stratton, J. A., Electromagnetic Theory. New York, 
McGraw, 1941. (See p. 563) 

and Houghton, H. G., "A Theoretical Investigation 

of the Transmission of Light Through Fog." Phys. Rev., 
38:159-165 (1931). 

Waldram, J. M., "Measurement of the Photometric 
Properties of the Upper Atmosphere." Trans. Ilium. 
Engng. Soc. London, 10:147-188 (1945). 

"Measurement of the Photometric Properties of the 



40 



41 



42 



43 



44 



45 



46 



47 



48. 



49. 



VISIBILITY IN METEOROLOGY 



97 



Upper Atmosphere." Quarl. J. R. meteor. Soc, 71:319- 
336 (1945). 

50. Disappearance Range Gauge. General Electric Co. Res. 

Lab. Rep. No. 8672, Wembley, Eng., May 23, 1945. 

51. WiGAND, A., 'Ein Methode zur Messung der Sicht." 

Phijs. Z., 20:151-160 (1919). 

52. Wright, H. L., "The Size of Atmospheric Nuclei; Some 

Deductions From Measurements of the Number of 
Charged and Uncharged Nuclei at Kew Observatory." 
Proc. phys. Soc. Land., 48:675-689 (1936). 

53. "Atmospheric Opacity: a Study of Visibility Observa- 



tions in the British Isles." Quart. J. R. meteor. Soc, 
65:411-439 (1939). 

54. "Sea-Salt Nuclei." Quart. J. R. meteor. Soc, 66:3-11 

(1940). 

55. "The Origin of Sea-Salt Nuclei." Quart. J. R. meteor. 

Soc, 66:11-12 (1940). 

56. "Atmospheric Opacity at Valentia." Quart. J. R. 

meteor. Soc, 66:66-77 (1940). 

57. Zanotelli, G., "Assorbimento elementare della luce nel 

passagio attraverso alle nubi." Atti Accad. ital., Rend 
CI. Sci. fis. mat. nat., 2:42-50 (1940). 



i 



ATMOSPHERIC ELECTRICITY 

Universal Aspects of Atmospheric Electricity by 0. H. Gish 101 

Ions in the Atmosphere by G. R. Wait and W. D. Parkinson 120 

Precipitation Electricity by Ross Gunn 128 

The Lightning Discharge hy J. H. Hagenguth 136 

Instruments and Methods for the Measurement of Atmospheric Electricity 

by H. Israel 144 

Radioactivity of the Atmosphere by H. Israel 155 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 

By O. H. GISHi 
Lincoln, Nebraska 



One becomes aware of weather through sensibility 
to heat or cold, calm or storm, brightness or gloom, but 
one's unaided senses do not reveal the ever-present uni- 
versal aspects of atmospheric electricity. Of course one 
sees lightning and hears thunder, but these are heralds 
of an impetuous, stormy aspect of atmospheric elec- 
tricity which is not universal. Lightning is seldom seen 
in the polar regions and even in temperate latitudes it 
is seen only a small fraction of the time. The study by 
Brooks [8] indicates that on one-fourth of the earth's 
surface thunder may be heard on less than one daj' in 
a hundred. 

But everywhere on the earth, electric forces in the 
open atmosphere are readily detectible with instru- 
ments. Many measurements made in most representa- 
tive regions of the earth show that (1) during fair 
weather the average electric field strength or potential 
gradient is usually more than 100 volts per meter, (2) 
the electric potential increases with elevation above the 
surface but the field strength, or the potential gradient, 
decreases, and (3) the direction of the electric field in 
fair weather is such that positive ions in the air drift 
towards the earth and negative ions di'ift away. One 
must infer from these observations of the electric field 
that the electric charge on the surface is always negative 
everywhere on the earth, except in the vicinity of 
thunderstorms or where drifting dust or some other 
local charge-generating process temporarily disturbs the 
normal aspect. 

Another fact of fundamental importance is that air, 
in the open, is not a perfect insulator: Although the 
electrical conductivity of air is so small that for most 
practical affairs it need not be considered, this property 
does play an important role in determining the electric 
state of the atmosphere. For example, because of this 
property and the existence of an electric field, an electric 
current flows from air to earth and the average magni- 
tude of this current, based on numerous measurements, 
is such that 90 per cent of the negative charge on the 
earth would be neutralized in thirty minutes. Despite 
this, the charge at the present time doubtless is about 
the same as it was one hundred years ago when Sir 
William Thomson (later Lord Kelvin) made the first 
reliable quantitative measurements of electric field 
strength. 

How is the negative charge of the earth or the corre- 
sponding electric field maintained? or, in other words. 
How and where is negative electricity supplied to the 
earth at the rate required to compensate, on the aver- 
age, for the loss by electric conduction? Many attempts 



1. Retired from Department of Terrestrial Magnetism, 
Carnegie Institution of Washington. 



to answer this question have been made since the prob- 
lem was first recognized, about the beginning of this 
century, but most of the answers have been definitely 
confuted. The challenge presented by this problem 
seemed to some to call for radical measures. Several 
eminent physicists thought that the answer might re- 
quire some modification of basic laws of physics or 
might depend on some physical entity or property that 
had not yet been discovered [1]. These nonclassical sug- 
gestions were made at a time when all other proposals 
seemed inadmissible, but since then some evidence has 
been found which lends support to the suggestion that 
thunderstorms supply negative electricity to the earth 
at a rate which is adequate to maintain the negative 
electric charge of the earth and the electric field of the 
atmosphere. 

According to this view, each thunderstorm which 
has developed sufficiently acts as a generator of elec- 
tricity and all the thunderstorms of the earth, acting as 
generators connected in parallel between the earth and 
the high atmosphere, provide the supplj^ current which 
maintains the high atmosphere at a potential of several 
hundred kilovolts positive with respect to the earth. 
The requirements which this supply current must 
satisfy will be seen better after the review, which fol- 
lows, of the chief universal aspects of atmospheric 
electricity, but from what has already been said it will 
be e^'ident that the more general requirements are (1) 
the supply current generated in the thunderstorms must 
flow upward into the high atmosphere and then spread 
out and return to earth as a more or less uniformly dis- 
tributed air-earth conduction current, (2) the magni- 
tude of the supply current must equal the total current 
from air to earth in all fair-weather areas of the earth, 
and (3) the variations of the total supply current should 
correspond to the \'ariations in the total air-earth cur- 
rent. Whether or not the net electric current which flows 
betA\-een the earth and thunderstorms meets these re- 
quirements has not been definitely ascertained because 
the electrical circumstances under thvmderstorms are 
so complex that it has not been feasible to make the 
measurements which are needed. 

The foregoing requirements are clearly indicated by 
extensive measurements of air-earth current density 
which have been made in representative areas of the 
earth, and it is from these measurements that the 
magnitude and characteristics of the supply current 
may now be inferred. 

Values of the air-earth electric current density i, al- 
though very small, have been obtained satisfactorily 
at several places for a number of years by automatic 
registration. The value of i may be obtained either (1) 
by a "direct" method [19] in which the current is "col- 
lected" on an insulated plate set flush with the earth's 



101 



102 



ATMOSPHERIC ELECTRICITY 



surface, or (2) by an indirect method- which involves 
the measurement of three factors : (a) potential gradient 
or electric field strength E, (b) the electrical conductiv- 
ity of the air attributable to the positive ions Xi, and 
(c) the conductivity attributable to negative ions X2. 
The electric current density then is obtained from the 
relation 



i = (Xi + \,)E. 



(1) 



The sum (Xi + X2) = X will here be called the total 
conductivity, or simply conductivity when the latter en- 
tails no ambiguity. The technique for making automatic 
registrations of these three factors is now more satis- 
factory than that for registration by the direct method. 
This, and the advantage for analytical purposes of 
knowing how the several factors vary, is the reason that 
the indirect method has been used in most long series of 
registrations. 

ELECTRICAL CONDUCTIVITY OF AIR 

The conduction of electricity in air and other gases 
became a concrete conception in the last years of the 
nineteenth century. Coulomb found in 1785 that an 
electrically charged body when exposed in air loses 
charge at a rate given by the law which bears his name. 
However, his discovery received little attention until 
1887 when W. Linss made measurements, two times 
each day for two years, of the proportional rate of 
dissipation, or the coefficient of dissipation a, of elec- 
tricity from a charged body exposed in the open air. 
The coefficient a is defined by Coulomb's law, namely, 
dQ/dt = —aQ, where Q represents the quantity of 
electricity on the body and dQ/dt represents the rate 
at which charge is lost. These measurements showed 
that, in present-day terminology, (1) the electrical con- 
ductivity of air, which is roughly proportional to a, 
varies considerably from time to time, (2) it is greater 
in summer than in winter, and (3) during the year the 
conductivity on the average varies inversely as the 
potential gradient. This inverse relationship is fre- 
quently found. It implies that the electric conduction- 
current in fair weather tends to vary less than at least 
one of the two component factors, namely, potential 
gradient and conductivity. But at some places where 
the air conductivity is small the air-earth current den- 
sity is considerably less than normal. 

The conductivity of air was earlier thought to arise 
from' the presence of impurities, such as particles of 
dust, smoke, fog, or water in its various forms, until J. 
Elster and H. Geitel, about 1895, from their numerous 
measurements of electrical dissipation, showed the re- 
verse, namely, that air generally conducts electricity 
best when pure and relatively dry. These observations 
were clarified when the conception of gaseous ions was 
introduced near the end of the nineteenth century. 

But how are ions formed in the open air? Elster 

2. Methods of measuring the elements of atmospheric elec- 
tricity are described in the article in this Compendium by H. 
Israel entitled "Methods and Instruments for the Measurement 
of Atmospheric Electricity." 



and Geitel, in search for an answer to that question, 
discovered that the air over land generally contains 
radioactive matter, that most of the important con- 
stituents of the earth's crust contain measurable 
amounts of radioactive matter and that the former is 
doubtless derived from the latter. Since it had recently 
been found that radiations from radioactive substances 
form ions in the surrounding air, the conductivity of 
the air over land, but not of that over the oceans, 
seemed to be largely accounted for. 

The first clue of the ionizing agent which is active 
at sea appeared when Elster and Geitel and C. T. R. 
Wilson in the first years of this century found that air 
from which radioactive matter had been carefully re- 
moved continued to be somewhat conductive. These 
observations apparently stimulated a series of investi- 
gations by other physicists, which eventually led to the 
discovery of what are now conunonly called cosmic rays. 
That these ionizing rays are of extraterrestrial origin 
was first clearly indicated by observations made by 
V. Hess (1911) during ten balloon flights. These obser- 
vations were verified and extended by W. Kolhorster 
in 1913. 

Beginning in 1915 many measurements of the cosmic 
radiation were made on all oceans during cruises of the 
Carnegie. These showed that the intensity is about the 
same at sea as at sea level on land. Furthermore, meas- 
urements over the open seas showed that there the 
radioactive content of air is not more than two per cent 
of that found on the average over land. Other measure- 
ments made on these cruises showed that the amount of 
radium in sea water, far from land, is less than one per 
cent of the amount found in the soil. The results of 
these observations strongly corroborated those of Hess 
and Kolhorster and showed that this radiation is doubt- 
less of universal distribution and constitutes the pre- 
ponderant ionizing agent over the oceans. 

Furthermore, balloon observations of the several fac- 
tors involved indicate that everywhere in the tropo- 
sphere and stratosphere, at altitudes greater than one 
or two kilometers, the air is ionized almost exclusively 
by the cosmic radiation. This radiation is, accordingly, 
an all-important factor in determining the character of 
the universal aspects of atmospheric electricity. 

But this statement does not apply in the region above 
the stratosphere, namely, the ionosphere extending up- 
ward from an altitude of 60 km. There the electrical 
conductivity is much greater than would prevail if 
cosmic radiation were the only ionizing agent. The in- 
tense ionization of the ionosphere is attributed to ultra- 
violet light and corpuscular radiation from the sun. 
Perhaps the comparatively great electrical conduc- 
tivity in the lower part of the ionosphere plays a part 
in promptly distributing the supply current from the 
thunderstorms to remote areas over the earth, but this 
has not yet been proven. This distribution may occur 
at a lower level. 

Since, aside from the possibility just mentioned, the 
ionosphere is presumably not involved in the phe- 
nomena which are usually regarded as belonging in the 
category of atmospheric electricity, the interesting elec- 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



103 



trical properties of that region will not be discussed 
here. This subject is treated in references [1] and [5]. 

Without the conductivity of the troposphere and 
stratosphere, which depends chiefly upon the cosmic 
radiation, atmospheric electrical phenomena would un- 
doubtedly be very different, and the universal distribu- 
tion of the fair-weather electrical phenomena that are 
now obser\'ed would doubtless not occur. 

At sea level the cosmic radiation forms ions in pairs, 
one positively the other negatively charged, at a rate, 
depending upon magnetic latitude, of 1.5 to 2.0 ion- 
pairs per cubic centimeter per second. This is practically 
the complete rate of ion formation over much of the 
ocean area and doubtless also over land in the polar re- 
gions, but in the lower atmosphere over most land areas 
the birth rate of ions is several fold greater than this on 
account of the additional ionization there by radioactive 
matter. The magnitude of the ionization rate near the 
earth over land is not readily determined and estimates 
vary between wide limits, but 10 ion-pairs per cubic 
centimeter per second may perhaps be taken as an ap- 
proximate representative average value. 

Despite the greater rate of production of ions, the 
electrical conductivity of the air over land generally 
does not exceed that at sea, and at some places, es- 
pecially near large cities, it is much less. For example, 
in the outskirts of Washington, D. C, it is about one- 
seventh the value at sea. This apparent paradox was 
resolved when it was found that in air which contains 
certain impurities, the normal small ions are trans- 
formed into large ions which drift more slowly in the 
electric field and thus contribute less to the conductiv- 
ity. These large ions are indeed so very sluggish that if 
all the small ions were transformed in this way the 
conductivity would be reduced to a very small fraction 
of the normal value. 

The electrical conductivity of a gas which contains 
ions of various types may be expressed as 



X = e "^kirii, 



(2) 



where e is the electronic charge, k is the ionic mobility, 
and n is the concentration of ions of each type. All 
ions are here assumed to carry a single electronic charge. 
The mobility varies as the inverse of the density of the 
gaseous medium and depends upon several factors in- 
cluding the character of the ion species, the sign of the 
ionic charge, and the "size" of the ion. Values ranging 
from 0.0003 to 0.0007 cm^ v-^ sec-^ for the mobility of 
large ions have been reported, whereas an average value 
for the small ions in the atmosphere at sea level is 
about 1.4 cm^ v~' sec~', but the standard deviation of 
these values is rather large. Measurements made in the 
laboratory indicate that the mobility of the negative 
ion in air is about 1.3 times that of the positive ion. 

Since in the atmosphere the large ions appear to be 
formed chiefly at the expense of small ions, the air 
conductivity is reduced when air is polluted with sub- 
stances such as some products of combustion, which 
occur as molecular aggregates with a diameter of the 
order of 10""'' cm. These, upon capturing small ions, be- 
come large ions with such low mobility that they play 



an insignificant role in the conduction of electricity. 
The result of this is that the conductivity is reduced be- 
cause the terms kn (equation (2)) which apply for small 
ions are decreased more than the corresponding terms 
for large ions are increased. 

The concentration of small ions n, when equilibrium 
is established between the rate of production and the 
rate of destruction, is given approximately by the rela- 
tion 

g = an^ -f (SnN, (3) 

where q is the rate of production of small ions (ion-pairs 
per cubic centimeter per second) ; n is the concentration 
of small ions, either those positively charged or those 
negatively charged; N is the concentration of the posi- 
tively charged, the negatively charged, and, the elec- 
trically neutral large-ion constituents; a is the coef- 
ficient of combination for small ions, with a value, at 
standard temperature and pressure, of about 1.6 X 10~^; 
;8 is a parameter whose value is of the same order as 
that for a, but this value apparentl}^ depends upon 
some factors which are not yet identified. An average of 
values for /3 determined from the data of Cruise VII of 
the Carnegie is about 2 X 10-" [20]. 

In deriving this form of the ionic equilibrium relation, 
which is a simplification of more general relations [15],' 
assumptions have been made which restrict its applica- 
tion. But in many cases where the data used for N are 
the values measured with an Aitken nuclei counter, 
and those for n are the measures of small ion concentra- 
tion, this equation seems to be satisfied. The term con- 
taining N in (3) usually is dominant in the lower at- 
mosphere over land and, especially in the vicinity of 
large cities, the term in n- is negligible, but at altitudes 
greater than 1 or 2 km in the free atmosphere, the latter 
term apparently is dominant during fair weather. These 
two terms are of about equal importance for the average 
conditions which prevail in the air near the surface over 
the oceans {N about 2000) . Thus the equilibrium value 
of n is given by n = y/ qia for clean air and by n = 
q/{pN) for air that is polluted with many Aitken nuclei. 
The magnitude of air conductivity X not only ^^aries 
from place to place at sea level but it also varies from 
time to time. The average value of X measured over the 
oceans on Cruise VII of the Carnegie was 2 X 10"'' 
stat mho. Values over land are sometimes greater than 
those over the oceans, but smaller values are found at 
most places where measurements have been made. 
These values for land are so variable that an average 
has little significance. At Kew Observatory in the 
vicinity of London, X appears to be about one-twelfth 
the value at sea and the variations are dependent to a 
large extent upon the varying pollution of the air. At 
the Huancayo Observatory near Huancayo, Peru, lo- 
cated at an altitude of 11,000 ft in a valley between 
ranges of the Andes mountains, the average X is large-— 
about three times the average for the oceans — but it is 
less than should be expected for a station at that alti- 



3. Consult "Ions in the Atmosphere" by G. R. Wait and 
W. D. Parkinson, pp. 120-127 in this Compendium. 



104 



ATMOSPHERIC ELECTRICITY 



tude even if cosmic radiation were the only ionizing 
agent. At Huancayo, X undergoes an 80 per cent de- 
crease in about one hour between 6 and 8 a.m. during 
the dry season (Fig. 5). The low value continues during 
the daylight hours and is followed by a gradual increase 
which begins at about sunset. The abrupt decrease of X 
is accompanied by a corresponding increase in the 
count of Aitken nuclei. 

Apparently on the days when this occurs a shallow 
stratum of very stable air is established at night. The 
nuclei, initially present in the air near the surface, 
coalesce and settle out during the night and any radio- 
active matter exhaled from the ground is entrapped. 
Thus there are two factors which tend to gradually in- 
crease the conductivity at night. In the morning when 
the stable air layer breaks up and mixing sets in, nuclei 
presumably come down from the higher air and such 
radioactive matter as may have been entrapped is dis- 
persed throughout a greater depth of air. Measurements 
indicate that the rate of ionization in daytime is about 
80 per cent of that for nighttime at this station. Ac- 
cordingly, the greater part, about 80 per cent of the 
abi'upt decrease of X in the morning, is attributable to a 
corresponding increase in the pollution of the air by 
substances which can form ions which drift very slowly 
in the earth's electric field. 

These are examples of the kind of information now 
available which seems to justify the statement that 
most of the large changes of air conductivity, not only 
changes with time but also with position, are asso- 
ciated with changes in the purity of the air. 

Temperature and pressure, although important fac- 
tors where change of altitude is involved, effect only 
minor changes in air conductivity at sea level. The fact 
that the conductivity is greater in summer than in 
winter at a number of places may be attributable partly 
to a temperature effect. Calculations indicate, however, 
that for an annual temperature range of 30C, the cor- 
responding range of conductivity for pure air would be 
18 per cent of the mean, but the actual range is much 
greater than this — other factors apparently are in- 
volved. 

Some observations indicate that the content of radio- 
active matter in the air over land is greater in summer 
than in winter and the greater conductivity in summer 
is probably in part a consequence of this, but the in- 
formation about the annual variation of the radioactive 
content of air, or about the rate of ion formation g, is at 
present insufficient for making an appraisal of the quan- 
titative importance of this factor. One would expect an 
effect of this kind only in regions where the exhalation 
of radioactive matter from the soil is hindered more 
during the winter season than during summer, owing 
to the prevalence of such conditions as a snow cover, 
frozen damp soil, or unfrozen waterlogged soil. The 
chief part of this annual variation of X in the vicinity 
of large cities is attributable to a corresponding varia- 
tion in the pollution of the air and there is some evidence 
that this factor plays a dominant part in effecting the 
annual variation of conductivity at most places on land 
where observations have been made. 



The air conductivity near the earth is also affected by 
the electric field. During normal weather the concen- 
tration of negative ions near the surface decreases as 
the field strength increases. This occurs because nega- 
tive ions drift away from the earth when the potential 
gradient is positive (field strength negative) and few, 
if any, such ions are supplied to the air from the earth. 
This effect of the electric field upon air conductivity 
is very pronounced when, as during storms, the field 
strength is large. Examples are given in Figs. 4 and 6. 
In Fig. 6, beginning at about 14^ the negative con- 
ductivity (X2) is negligible during most of the follow- 
ing hour while the positive conductivity (Xi) is about 
normal. But shortly after 15''15'", X2 abruptly returns 
to a normal value and at the same time Xi almost van- 
ishes. This condition continues for about fifteen 
minutes, then, at 15''30"', X2 again vanishes and Xi re- 
turns to a normal value. Six other such alternations 
occur before the storm ends at about 17''20'". 

Most of the changes of the electric field, which cause 
these marked changes in conductivity, are not clearly 
seen on the electrogram for potential gradient in Fig. 
6. That correspondence is better illustrated in Fig. 4 
during the interval O** to 3'' when the electric field, being 
less intense, was clearly recorded most of the time. 

Many of the changes of air conductivity are not ac- 
companied by noticeable changes in air-earth current 
density. It is only when the change in conductivity ex- 
tends throughout a considerable range of altitude that a 
marked correlation is seen. These cases must be taken 
into account when one is examining data for the broader 
universal aspects of atmospheric electricity. For ex- 
ample, in estimating the magnitude and the character of 
the variations of the supply current from measurements 
of i, allowance must be made for abnormalities which 
depend wholly upon local circumstances. The most sig- 
nificant of these abnormalities, for areas of fair weather, 
depend upon local modifications of the distribution of 
air conductivity with altitude. 

Air conductivity depends upon altitude in a com- 
plicated way. The value at an altitude of 18 km (60,000 
ft), during the notable flight of the balloon Explorer II, 
was 100 times the average for sea level. The chief factors 
involved here are (1) the intensity of cosmic radiation 
increases with altitude, (2) the rate of ion formation for 
a given ionizing radiation decreases directly as the air 
density, (3) the mobility of the ions varies inversely 
as the air density, (4) the rate of ion destruction in pure 
air of a given ion concentration decreases with altitude, 
varying directly with the y^ power of pressure (ap- 
proximately) and inversely as the ,^3 power of absolute 
temperature, (5) the concentration of radioactive mat- 
ter exhaled from the earth over land decreases with 
altitude, (6) the pollution of the atmosphere usually de- 
creases with altitude, and (7) the dependence of fi 
(equation (3)) upon temperature and pressure doubt- 
less plaj^s a part of unknown magnitude in determining 
the variation of X with altitude in the lowest kilometer 
or so. 

The last three factors apparently are relatively in- 
significant at altitudes greater than one or two kil- 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



105 



ometers during normal weather but, in the vicinity of 
storms, effects which may be attibuted to these factors 
(particularly the last two) were observed by 0. H. Gish 
and G. R. Wait at considerably higher altitudes. 

The rate of ion formation q, when cosmic radiation is 
the only ionizing agent, depends on factors (1) and (2). 
Values for g as a function of altitude are shown in Fig. 1. 
These computed values are based on observations of 
cosmic radiation reported by Bowen, Millikan, and 
Neher and on average data for temperature and pres- 
sure for each of the two latitudes. The value of q in- 
creases from a low value at sea level to a maximum at 
an altitude of 12 to 13 km. The maximum for the higher 
latitude is more than two times that for the lower lati- 
tude. 



28 


\ 


1 


1 '■ 


1 




, \ 


\ 






- 


20 

16 


\ 


V; 


-OMAHA, I 
(MAGNET 


J.S.A. 

C LATITUD 


E 5I°N) _ 


- ^ 


\ 






- 




>v 






\ 


12 
8 


- 


N 


MADRAS, 
(MAGNETIC 


NDIA 
LATITUDE 


S'N) j 


- 


/ 






y 




/ ^ 


-■^ 






4 





/^ 








// 
/ / 

" / / 
/ / 


1 


1 


1 


- 



10 20 

RATE OF ION FORMATION 



30 
(ION-PAIRS 



40 
CM" 



' SEC') 



50 



calculated from measured values of cosmic radiation and 
of temperature and pressure, the latter two observed 
during the flight. During this flight the conductivity in- ■ 
creased from the surface up to an altitude of 18 km 
(60,000 ft) where it was about 100 times the value at the 
surface. In the altitude range 18-22 km, it varied ir- 
regularly but in general decreased with altitude. This 



Fig. 1. — Rate of ion formation by cosmic radiation for 
middle and low latitudes. (From data of Bowen, Millikan, and 
Neher.) 



An increase of conductivity with altitude was first 
shown by measurements of X made on twelve balloon 
flights during the period 1905-20. Eleven of these 
started in Germany and one in Russia. The maximum 
altitude at which measurements were made was less 
than 6 km except for one in which it was nearly 9 km. 

Continuous registration of X up to a maximum alti- 
tude of 22 km was made during the flight of the strato- 
sphere balloon Explorer II [14]. The results for this 
flight are shown in Fig. 2. The crosses on graph .4 
represent direct measurements of Xi, and the circles 
represent values derived from direct measurements of 
X2 by multiplying the latter by 0.78. This factor is the 
ratio of the mobility of positive ions to the mobility of 
negative ions. The smooth graph B represents values 



70 



60 



wi 50 



40 



30 



CD 20 




10 







20 



4 



i 



LEGEND 



A-POSITIVE CONDUCTIVITY FROM 
REGISTRATIONS DURING DESCENT., 

•POSITIVE CONDUCTIVITY CALCU- 
LATED FROM OBSERVATIONS OF 
COSMIC RADIATIONS, ASSUMING 
THAT SMALL IONS ALONE ARE 
INVOLVED. 



15 



10 < 



5 F 



20 



80 

-4 



100 



40 60 

X IN UNITS OF lO"" ESU 
Fig. 2. — Air conductivity, flight of Explorer 11 near Rapid 
City, South Dakota, November 11, 1935. 

last feature may be attributed to the presence there of 
substances (perhaps Aitken nuclei) which served for the 
formation of large ions. This decrease of conductivity 
is in the same region where ozone was simultaneously 
found to be especially abundant. Whether this feature 
is universal, whether it is generally associated with 
ozone, and whether there are factors in the atmosphere 
at j^et higher levels which eff'ect a similar diminution 
of the conductivity are c^uestions which have important 
bearing on other than electrical aspects of the atmos- 
phere. Therefore, further investigation of the con- 
ductivity of the high atmosphere is called for. At 
present, there is indirect evidence which indicates that 
this diminution of conductivity at high levels is either 
not universal or else is rather limited in vertical extent. 
The unexplored region to which this statement applies 
extends from 22- to about 60-km altitude. Above 60 
km the concentration of ions has been determined at a 
number of places on the earth by quantitative studies 
of the "reflections" of radio waves. Such observations 
demonstrate that the air above that level is extraordi- 
narily conductive. 

Other measurements of X up to an altitude of over 14 



106 



ATMOSPHERIC ELECTRICITY 



km (48,000 ft) were made in 1948 by Gish and Wait 
during ascent or descent for electric surveys over 
thunderstorms (a joint project of the U. S. Air Force 
and the Department of Terrestrial Magnetism of the 
Carnegie Institution of Washington). These unpub- 
hshed values are on the whole consistent with those 
shown here except that they tend to be smaller.* 

The values of X versus altitude, shown in graph B 
(Fig. 2) were calculated for the case in which the air 
contains no large ions and the cosmic radiation is the 
only ionizing agent. The agreement between these and 
the measured values is one of the considerations which 
leads to the conclusion that throughout much of the 
high atmosphere pollution is negligible and cosmic ra- 
diation is the chief ion-producing agent. 

The relatively large air conductivity at high alti- 
tudes and the increase with altitude are features upon 
which sevei-al other aspects of atmospheric electricity 
depend. For example, (1) the suggestion that thunder- 
storms are the source of the supply current could not be 
seriously considered if X were not a rapidly increasing 
function of altitude, and (2) the decrease of electric 
field strength with altitude and the character of the 
diurnal variation and that of some of the other varia- 
tions of field strength depend on these aspects of X. 

For cases in which the electric field strength or the air- 
earth current, or both, depend upon the over-all effect 
of the conductivity throughout a vertical column of the 
atmosphere, it is convenient to use the concept of elec- 
tric resistance, rather than electric conductance, of the 
column. 

The resistance of a vertical column of the atmosphere of 
1 cm- cross section and extending from the earth's sur- 
face up to a certain height is obtained by integrating the 
reciprocal of X from the surface up to that height. A 
value of "columnar resistance" r, obtained in this way 
from the values of X shown in Fig. 2, is lO'"^ ohms for a 
column extending from sea level to an altitude of 18 
km. If this is regarded as representative for the whole 
earth, the total effective resistance R from the surface 
to the 18-km level would be 200 ohms. Most of this 
resistance is offered by the lower part of the column. 
The highest eight kilometers contribute only five per 
cent of the total, whereas the lowest two kilometers con- 
tribute 50 per cent. 

Estimates of r up to altitudes considerably greater 
than 18 km, based on observed values of cosmic-radia- 
tion intensity and the indicated trend of that radiation 
at altitudes not yet explored, indicate that the value of 
r for a column extending up to the ionosphere would not 
exceed by more than 10 per cent that for 18 km, pro- 
vided the small ions at those higher levels are not trans- 
formed into larger, less mobile types, in appreciable 
number. Such estimates may at least set a lower limit 
for r between the earth and the ionosphere. An upper 



4. Subsequent to the preparation of this article, results of 
the measurements described above have been published and 
will be found in "Thunderstorms and the Earth's General 
Electrification," by O. H. Gish and G. R. Wait, J. geophys. Res., 
55:473-484 (1950). 



limit, not exceeding by as much as 50 per cent the 
value up to an altitude of 18 km, seems to be indicated 
by the extent to which air pollution of local origin — ■ 
say from a city like Washington, D. C. — diminishes the 
air-earth conduction current through diminution of air 
conductivity in the lower atmospheric strata. 

The columnar resistance is apparently 15 to 20 per 
cent greater near the equator than in middle latitudes, 
owing chiefly to a dependence of the vertical distribu- 
tion of cosmic-radiation intensity upon latitude (Fig. 1). 
This is of interest here because it provides an explana- 
tion of the tendency, found by S. J. Mauchly, of the 
potential gradient measured at sea to be about 17 per 
cent less in the equatorial belt than in belts of higher 
latitude, whereas the air conductivity at the surface was I 
found to be practically independent of latitude. This 
variation of r with latitude is not, however, as large as 
the variation from place to place on land. Over an 
urban area the value of r may be several times that in 
the relatively pure air over open country. 

When all these circumstances are considered, it seems 
likely that an average value of r is about 10-^ ohms and 
that the effective resistance R over all fair-weather 
areas of the earth is not far from 200 ohms. Here R is 
equivalent to r/S where S is the area of the earth. It is 
assumed here that the total area over which electrical 
storms are in progress at a given instant is negligible — 
the data for thunderstorms of the earth collected by 
C. E. P. Brooks indicate that the total storm area is 
usually less than O.OOSjS. 

The electrical conductivity of air in the ionosphere is 
apparently so great that electric fields there must be 
very small and can be disregarded in this discussion. 
No direct measurements of X have been made in the 
ionosphere, but a reliable estimate of the order of magni- 
tude is obtained by using the measurements, made by 
"radio" methods, of the equivalent ion density, to- 
gether with estimates of air density at the corresponding 
altitudes. The value for X, estimated in this way for an 
altitude of 70 km, near the lower boundary of the 
ionosphere, is about 10' stat mho cm~\ or the resistiv- 
ity, the reciprocal of conductivity, is less than 10^ ohm 
cm. According to this estimate, the relaxation time, 
namely l/(47rX), at this altitude is less than 10~* sec. 
This means that a local concentration of free electric 
charge cannot persist here for an appreciable time; it 
would, indeed, be diminished to 0.01 per cent of the 
initial value in 0.1 ^sec. 

Similar circumstances occur in the earth: The re- 
sistivity of most of the material near the earth's surface 
is less than that for air in the lower ionosphere — that of 
ocean water is less than 100 ohm cm. Even for geologi- 
cal structures where the highest values of earth-re- 
sistivity (10^ to 10' ohm cm) have been measured, the 
relaxation time is of the order of microseconds. In con- 
trast to this, the relaxation time for air near sea level is 
generally greater than 400 sec while for air at 18-km 
altitude it is about 4 sec. Because of these circumstances 
it seems permissible to describe the world-wide aspects of 
atmospheric electricity with the aid of a spherical 
condenser model as follows. 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



107 



The earth and the ionosphere, or possibly the upper 
stratosphere, serve as the inner element and the outer 
element, respectively, of a spherical electrical condenser. 
Because the air between the inner and outer elements is 
conductive this condenser has a "leakage" resistance R. 
A difference of potential V between the elements is 
maintained by the supply current. The leakage current 
I is V/R, and for steady conditions this is also the 
magnitude of the supply current. For / = 1800 amp 
and R = 200 ohms (values based on observations), V 
= 360,000 V. A somewhat lower value of V is obtained 
from measurements of potential gradient made on bal- 
loon flights at altitudes ranging from sea level to about 
10 km (see equation (4)). 

Apparently I and V are the chief variables in this 
relation and of these V is regarded as the independent 
variable. No appreciable variation in R is indicated by 
the data now available. Although the average con- 
ductivity measured on Cruise VII of the Carnegie (mean 
epoch, 1929) was only 74 per cent of that for Cruise 
VI (mean epoch, 1921), the average air-earth current 
density did not differ significantly, that for Cruise VII 
being 107 per cent of the value for Cruise VI. This 
indicates that /, and consequently V/R, was essentially 
the same for these two epochs. This fact does not neces- 
sarily exclude the possibility that V and R were related 
as dependent and independent variables, respectively, 
because if R had increased but the supply current had 
remained constant, T' would have varied directly as R. 
But there are no grounds for thinking that R varies ap- 
preciably owing to variation throughout the atmosphere 
in the rate of ionization, the chief factor. The chief 
ionizer, the cosmic radiation, seldom varies by more 
than a few per cent of the mean; variations in ampli- 
tude as great as 3 to 4 per cent occur infrequently, 
usually during magnetic storms, and last only from a 
few hours to a day or two. On only four occasions in 
more than a decade have increases of more than 10 
per cent of normal (at sea level) been observed [12]. 
Perhaps on these occasions a detectible decrease in R 
occuiTed. This should be revealed by a simultaneous 
increase of X at widely distributed stations and a cor- 
responding decrease of E. No such world-wide changes 
of X and E have yet been definitely detected, but a 
special examination should be made of the four cases 
just mentioned. 

Apparently the only possible source of world-wide 
changes in X, amounting to more than a few per cent 
and continuing for long periods, is corresponding 
changes in the pollution of air with nuclei which serve 
for the formation of large ions. Even if such extensive 
changes do occur near the earth's surface, there would 
be no comparable change in R unless the change in X 
occurs throughout most of the troposphere. A decrease 
of X from the surface to a considerable altitude appar- 
ently does occur over limited areas especially in the 
vicinity of cities or industrial centers where there is 
notable pollution of the atmosphere. The extent of this 
is such that the columnar resistance r appears to be 
increased severalfold but the total area involved is 
doubtless such a small part of the earth's surface that 



only immeasurable effects in R may be expected. Pe- 
riodic changes in r, such as diurnal variations, are also 
in evidence at some places, but these depend mainly 
upon local circumstances and apparently do not affect 
R appreciably. 

These statements about variations in ?• are based on 
information obtained by an indirect method which de- 
pends upon the assumption that ir = F is the same 
everywhere on the earth at a given instant. If i is 
measured simultaneously at two places, then according 
to this condition the ratio of the value of r at one place 
to that at the other place is equal to the inverse ratio 
of corresponding values of i. The efficacy of this method 
of analyzing such data also depends upon the circum- 
stance that at some places, notably over the oceans, r 
seems to be much more nearly constant than at some 
places on land. This device has been used chiefly for 
estimating the average diurnal variation of r [21, 22]. 
The results are at least plausible. 

That the more prominent variations of X occur chiefly 
in the lower part of the atmosphere is indicated by the 
reciprocal relation, frequently found, between X and E 
(electric field strength), namely, XE = i where i is 
approximately constant. This indicates that in these 
cases r is not modified much by the changes in X, and 
that accordingly the vertical extent of the changes in 
X and E is relatively small. The height of the air stratum 
involved has been estimated in several ways. At Paris a 
height of 200 m or less was indicated by the observa- 
tion that variations of E near the top of the Eiffel 
Tower were chiefly of the universal type, whereas at a 
nearby ground station the variations were much more 
complex. Heights for the region of abnormal conductiv- 
ity of the order of one to two kilometers have been 
estimated for other situations, in which r is appreciably 
modified. 

Of the features of air conductivity discussed here, 
those of chief importance for the broader aspects of 
atmospheric electricity are (1) electrical conductivity of 
air is a universal property, (2) this property increases 
with altitude and at some altitude, probably less than 
60 Ion above sea level, is .so great that at a given instant 
the electric potential at that level is essentially the same 
everywhere over the earth, and (3) the electrical con- 
ductance between the earth and the high atmosphere, 
or the reciprocal of this, the resistance /?, probably is 
not subject to appreciable variation. 

THE ELECTRIC FIELD OF THE ATMOS- 
PHERE IN FAIR WEATHER 

Many observations of the electric field in the atmos- 
phere have been made during the nearly two hundred 
years since Franklin made his famous kite experiment 
in 1752 and Lemonier, later in that year, first observed 
an electric field in the atmosphere during clear weather. 
Before the end of the eighteenth century a number of 
the characteristics of the electric field were correctly 
inferred from qualitative observations made chiefly in 
Europe. Quantitative measurements of the electric field 
strength came into vogue after Sir William Thomson 
in 1860 stressed the need of measurements which could 



108 



ATMOSPHERIC ELECTRICITY 



be compared even though made by different observers 
and at different places. 

During this latter period, measurements have been 
made on most of the representative areas of the earth, 
including a number of series for the polar regions, many 
widely distributed measurements on the oceans, and 
measurements made during balloon flights (all in 
Europe) . Continuous registration has been used at most 
land stations since about 1910 and was also successfully 
employed at sea during Cruise VII of the Carnegie. The 
features of the electric field which are clearly shown by 
these data are as follows for fair-weather conditions. 

The electric field strength E is negative, or the potential 
gradient is positive, wherever and whenever fair weather 
prevails. The exceptions to this are rare and transitory. 
For example, a positive field (negative gradient) is 
registered while a dust whirl passes near the station. 
An example of such an effect appears on Fig. 5 between 
24h40in a^ji(j 14'>50'". Since at the surface of a conductor 
E = —dV/dZ = 4x0-, where dV/dZ is the potential 
gradient along the outwardly directed normal and o- 
is the surface charge density, one concludes that the 
charge of the earth in fair-weather areas is negative and 
that the potential of the air increases with altitude. 

The potential gradient (or —E) at the surface varies 
considerably from place to place. The average potential 
gradient at sea during Cruise VII of the Carnegie was 
130 V m~'. At some places on land an average consider- 
ably less than 100 v m""' has been reported, but values 
larger than that for the oceans are prevalent in densely 
populated areas: at the Kew Observatory near London 
the average value exceeds 300 v m~'. In the polar re- 
gions and in open country, far from sources of atmos- 
pheric pollution, the average is about the same as that 
for the oceans. Apparently a value of about 130 v m~' 
is a fairly representative average for the preponderant 
part of the earth's surface. 

The potential gradient decreases with altitude. The 
measurements of gradient made on 57 balloon flights, 
mostly over central Europe, as summarized by Schweid- 
ler [17], satisfy the following empirical equation: 

dV/dZ = 90 exp (-3.5^) -|- 40 exp (-0.232), (4) 

where dV/dZ is expressed in volts per meter for z, the 
altitude in kilometers. There is a sharp decrease from 
the surface up to about 1-km altitude followed by a 
slower decrease. The value at z = 0.5 km is less than 
half the value at the surface, and at z = 9 km it is less 
than 4 per cent of the surface value. The data for alti- 
tudes less than 1 km are scattered much more about 
the general trend than are those for higher altitudes. 
This may be due to variable pollution in the air near the 
earth, a circumstance that is indicated by other types of 
atmospheric electric observations such as the contrast 
between measurements of E made on the Eiffel Tower 
and of those made at a neighboring ground station. 

A decrease of E with altitude, if widespread and of 
the magnitude and character indicated by these data, 
doubtless is attributable chiefly to a corresponding in- 
crease of air conductivity. For these conditions \E = i 
is independent of altitude if the electric space-charge 



density p does not vary with time and provided convec- 
tion plays a negligible part in the transport of electricity 
in the atmosphere. The latter conditions doubtless are 
satisfied during most fair weather. The drifting of snow, 
or of dust, however, is accompanied by the generation 
and convection of electric charge and although this is a 
source of conspicuous modifications of the electric field 
near the earth on some occasions, for average fair- 
weather conditions the magnitude of electric convec- 
tion-current density calculated on the basis of available 
data is negligibly small. 

Measurements of both X and E were made on only a 
few balloon flights. For these the product \E was not 
invariable with altitude, but this result is probably at- 
tributable to a variation of the air-earth conduction 
current with either, or both, time and position [10]. 

The potential gradient of fair weather also decreases 
with altitude in the lowermost few meters owing to a 
depletion of the negative ions in this region, the so- 
called electrode effect. Under the action of the electric 
field, negative ions drift away from the earth and since 
such ions are not emitted from the earth at an appreci- 
able rate, the flux of negative ions, and accordingly the 
concentration, must vanish at the surface. But for 
steady conditions, the flux of positive ions from air to 
earth is nearly continuous in the lowermost few meters, 
and at the air-earth boundary is equal to the total elec- 
tric flux at higher levels. Two attending conditions are 

(1) positive ions predominate or a positive space charge 
prevails in air that is contiguous with the earth, and 

(2) the potential gradient decreases with altitude. These 
general aspects of the electrode effect may be modified 
or obscured when either or both the electric convection- 
current component and the displacement-current com- 
ponent are appreciable, or when the vertical distribu'^ion 
of air conductivity near the surface is abnormal. The 
conclusion that the electrode effect is a universal char- 
acteristic of the electric field of the atmosphere depends 
chiefly on the observed fact that X1/X2 is usually greater 
than unity in fair weather and that it increases as the 
gradient increases. 

The temporal variations of potential gradient are usually 
of complex origin, however there are types which may 
be classified on the basis of origin, as follows. From the 
several equivalent expressions for air-earth current den- 
sity, namely +\E and — I'/r, one obtains the relation 



E = -V/iXr), 



(5) 



which is valid except for the rather unusual condition 
that i is dependent upon altitude, or that the displace- 
ment current is appreciable. On this basis the follow- 
ing four types of change in E may be adopted: type 
(a) in which E is independent of V, X, and r, but X de- 
pends upon E; type (b) in which E °: 1/X, with V and 
r constant; type (c) for which E oc 1/r, while both X 
and V are constant; type (d) in which E o: V, while X 
and r are constant. In this discussion E and X are gener- 
ally used to denote values observed in air practically 
contiguous with the earth, V denotes the potential of 
the ionosphere (or upper stratosphere) relative to the 
earth, and r denotes the columnar resistance — the elec- 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



109 



trical resistance of a vertical column of air 1 cm^ cross 
section extending from the observation point up to the 
ionosphere. 

Variations of the first three types generally are 
marked by local characteristics ; many occur at irregular 
intervals but some follow a diurnal or other periodic 
routine, which varies much from place to place. The 
only thing in common among these variations is that 
usually factors of local origin tend to increase the gra- 
dient during daylight hours more than at night, but 
the contrasts in the amplitude and character of these 
variations at different places are remarkable. An ex- 
ample of the contrast between periodic local variations 
of this sort may be seen by comparing an electrogram 
for potential gradient (Fig. 3) obtained at the Watheroo 
Magnetic Observatory, Western Australia, with a cor- 
responding electrogram (Fig. 5) made at the Huancayo 
Magnetic Observatory near Huancayo, Peru (observa- 
tories established and operated by the Department of 
Terrestrial Magnetism of the Carnegie Institution of 
Washington). In the latter electrogram, the gradient at 



concentration of these nuclei increases rapidly between 
Q^ and 8^ in winter {3^ to 9'' in summer) and as a conse- 
quence X decreases; then as convection and turbulence 
increase during the day, the local contamination de- 
creases somewhat, and X increases; but when the air 
becomes more stable in the evening, local contamina- 
tion increases and X decreases again until checked when, 
after 20'', both the rate of introduction of the nuclei and 
their concentration decrease. Throughout the daylight 
hours the columnar resistance r increases to a maximum 
at about 19''. This doubtless indicates that the content 
of nuclei in the air column has been increasing during 
this period. A decrease of r which occurs during the 
night is doubtless the combined effect of (1) decreased 
rate of supply, and (2) scattering and other modes of 
dissipation of the nuclei. 

Potential gradient variations of type (a) are most 
prominent during stormy weather. Examples of such 
effects are exhibited in Figs. 4 and 6. These figures are 
reproductions of unretouched electrograms obtained at 
the Watheroo Magnetic Observatory and at the Huan 



■jUSr 29, 1936 



ISO £ AST MERIDIAN HOURS 
20 



-T^V^ 



POSITIVE CONOUCriVITY 



VEPITICAL SCALE IN UNITS OF 10''' CSU ? , .f ,.f , .f , 
I NEGATIVE coNodcrivify 



•p-~--U.,.i »|..»»»-U«-~ip~»»n 



rrrrprr 



V^.v** 



VERTICAL SCALE IN UNITS OF 10'" ESU 



*VV■V^l,•^''''A''J•^'■>■'•''*»■•V■•''■*''''■■V "'-^v'-V-.' 'v'.v.V *.■>'>>*>'« ■. 



POTENTIAL GRADIENT 



VERTICAL SCALE IN VOLTS PER METER 



Fig. 3.— Electrograms, Watheroo Magnetic Observatory, "quiet" day. 



8''30"' (local time) is about five times the value regis- 
tered two hours earlier. In the formei', there is a rela- 
tively small and gradual increase of gradient, beginning 
at about S'' local time and continuing throughout the 
daylight hours. The universal diurnal variation, which 
will be discussed later, is, of course, present in both 
these cases, but allowance for that would not change the 
order of contrast seen here. Analyses of such records 
from these two stations indicate to the author that the 
local aspect of the diurnal variation of potential gradi- 
ent at Watheroo is largely of type (c) while that for 
Huancayo is chiefly of type (6). 

At the Kew Observatory, where the influence of local 
air pollution is prominent, a semidiurnal variation of 
gradient of local origin appears with maxima at about 
8'' and 21'' local time. These apparently are a combina- 
tion of types (6) and (c) with type (6) dominant in the 
morning and type (c) coming into evidence later in the 
day [22]. The latter is an interesting example of a local 
influence which may be explained as follows. 

The introduction into the air in the general vicinity 
of the observatory of substances which serve as nuclei 
for the formation of large ions proceeds at an enhanced 
rate during the period 4'' to 20''. Near the surface the 



cayo Magnetic Observatory, respectively. Figures 3-6 
inclusive are samples selected from the thousands of 
such registrations made during the years 1922-46 at 
Watheroo and 1925-46 at Huancayo. Points for zero 
gradient are recorded each hour. Ordinates above this 
line of "zeros" correspond to positive values of gradient. 
During the 24-hr period of record shown in Fig. 4, three 
periods of rainfall were indicated by the station rain 
gauge. These are indicated at the top of the figure. The 
corresponding storm effects in potential gradient are 
exliibited in the lowest electrogram. Most of these were 
of moderate intensity on that day, and varied from 
positive to negative values of gradient. 

During the ten-minute period beginning at 18''10'" the 
gradient was entirely negative and at its greatest in- 
tensity exceeded 400 v m~', the limit of registration. 
During the period 0'' to 0''50'", several changes from 
negative to positive gradient occurred. The trace of 
these may not appear in the reproduction — the changes 
were rapid and the extreme values exceeded the limits 
of registration, namely, —400 and 700 v m"'. But for- 
tunately, in cases where the trace for potential gradient 
is not clearl}' shown, the sign of the gradient can usually 
be ascertained by an examination of the traces for con- 



no 



ATMOSPHERIC ELECTRICITY 



ductivity, because of the electrode effect previously dis- 
cussed. A characteristic of that effect is that a low 
value of negative conductivity and a normal value of 
positive conductivity should accompany a large posi- 
tive potential gradient, while for a large negative gradi- 
ent the roles of positive and negative conductivity 
should be interchanged. There is abundant evidence as 
well as a rational basis for this rule, but such evidence 
is not clearly shown in Figs. 4 and 6 during periods of 
greater activity because the original gradient trace was 
very dim when rapid changes of gradient occurred and 
was "off scale" for considerable periods. However, the 
reader doubtless can see evidence of trends of this char- 
acter in these figures. 



charge -cloud does not necessarily coincide with a visi- 
ble cloud. Ten such charge-clouds are indicated by the 
record for the latter storm. So many alternations of 
potential gradient in one series (barring changes which 
accompany lightning discharges and which are of too 
short duration to register with the apparatus used here) 
is somewhat unusual. They appear more frequently in 
records for the Huancayo station than in any other 
records available to the author. 

The suggestion that such a series of changes in gradi- 
ent may be attributed to a number of charge-clouds 
drifting by in tandem array may be an oversimplifica- 
tion. The only model of this sort which could account 
for the abrupt change of sign — within about one minute 



RAINFALL IN INCH 



AUGUST e, 19 je 



a 



— n^ooj 

ISO' EAST MERIDIAN HOURS 
kosmVE CONDUCTIVITY 



0.025^ (- \~-O.II— 
OjOS 



-AVCO 



0.02 — 1>- 
AUGUST 7, 1936 



ifS^pivi^' 



VERTICAL SCALE IN UNITS OF IQ-^ESU 9., .?. . .i :. .^ . . .9 . .V 



'"•^ 




' I'r" ■«^/* 



■A**^ 



VERTICAL SCALE IN UNITS OF KT^ ESU 9, i if , i ,f , i ,f , L.f.i.? 



POTENTIAL GftAOIENT: 




>tJ*l)J\ 




-yrrrc-f] 






. t/ERT/CAL SCALE IN VOLTS PER METER 'L- 



2<f0 . 



<l?0 



_600_ 



, ay 



Fig. 4. — Electrograms, Watheroo Magnetic Observatory, with periods of light rain. 



With the aid of this rule one can readily see that dur- 
ing the periods when intense electric fields prevail the 
sign of the gradient varies. The record shown in Fig. 6 
covers two storms in a 24-hr period : one in the interval 
20*" to 22"", approximately, on March 17, the other be- 
ginning about 14'' March 18 and lasting more than three 
hours. During the former period, a negative gradient 
was recorded for more than one hour but an intense posi- 
tive gradient for only 10 min is indicated. During the 
latter storm an intense positive gradient prevailed dur- 
ing the first 75 min. This was followed by an intense 
negative gradient which continued about 15 min. In 
the next hour and three-quarters, eight abrupt reversals 
of sign occurred. 

Such characteristics of potential gradient must be 
attributed to considerable masses of electric charge or 
"charge-clouds" in the vicinity of the observatory — a 



— and the intense field, continuing for 10-15 min or 
more between reversals, is one in which the charge- 
clouds are at an elevation which is small compared with 
their lateral dimension, and the array of clouds, charged 
alternately positive and negative, is closely packed. It 
is doubtful whether such a model is compatible with 
several physical conditions which seem to be required 
to maintain the charge of such clouds. Any further dis- 
cussion of phenomena of which this case is representa- 
tive should come under the category of the thunder- 
storm electric field, a topic which is discussed very 
briefly in this article. 

Another example of a field change of type (a) is 
shown on the trace for potential gradient in Fig. 5, just 
before Ui'SO™. This is a characteristic "dust whirl" or 
"dust devil" effect. The sign of the field change indi- 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



111 



JULY 6,193? 




■'», 






hm 



'S 



11 



?5 WEST MERIDIAN HOURS 

a 



JUL y 9. 1937 



12 



mi 



u^ 



I'lM 



■|f. 






ac 



kJCVi 






p5P<"B>ai k^T* ' 



i;i« 



t 



Fig. 5. — Electrograms, Huanoayo Magnetic Observatory, "quiet" day during dry season. 



RAINFALL ■ IfJ men 



MARCH 17^ 1937 
BO 



75 WEST MERIDIAN HOURS 
4 a 



MARCH la, 1937 
16 




VERTICAL SCALE IN UNITS OF XT' ESU ' ?■.■..?..'? 



POTENTIAL dRAOIENT 



v^: J , . |Uws4\wi 




Mil. 



1 



.r^^ 



VERTICAL SCALE IN VOLTS PER METER 1—. i . ^ . i ,J92-. 1 . ^9° . 1 .J3° 



Fig. 6.— Electrograms, Huancayo Magnetic Observatory, rainy day. (Note: Clearing in morning after las'"; early afternoon 
March 18, increasing cloudiness, distant rain, and thunder to southwest at 14''.) 

cates that the electric charge of the du.st in thi.s whirl- Watheroo Magnetic Observatory, are illustrated in Fig. 

wind is preponderantly negative. 3. This effect, apparently of type (a), is clearly cor- 

The relatively small and rapid variations of electric I'elated with wind strength and wind variability. Pre- 

field, which are common during daytime at the sumably the fine sand, prevalent in this semiarid region 



112 



ATMOSPHERIC ELECTRICITY 



of Western Australia, is agitated enough by the wind 
to introduce puffs of electric charge into the air near 
the surface. There is some evidence that small varia- 
tions of conductivity are associated with the field 
changes and the former are doubtless dependent on the 
latter. The drifting of snow, like the drifting of sand or 
dust, also modifies the electric field, but during the 
former, positive charge is introduced into the air. 

A description of field changes of types (a), (6), and 
(c) is relevant here chiefl3r because these phenomena 
must be recognized for what they are and must be dis- 
tinguished from the universal aspects of the electric 
field in order that the latter may be identified. 

Changes of type (a), which are prominent during 
storms, have importance for the clues they provide 



I ' ' I ' ■ I 

18 DAYS 




Ol40 

> 



X 34 DAYS 



— MEAN 140 ^^ 
N0V.-DEC^-_JAN^_^,-°'^,,-<-rr];f^^^7;^^ '' 
120=-^^ .^''^ ^^ 14 DAYS< 



100 



140 



120. 




inn lV^ 



Fig. 7. — Diurnal variation of potential gradient on the 
oceans, Carnegie Cruises IV, V, and VI, 1915-21 and Cruise 
VII, 1928-29. 



concerning the electrical constitution of storms, but 
changes of types (6) and (c) are of minor interest as 
geophysical phenomena, especially when thej^ depend 
upon the activities of man. 

The discovery of the universal diurnal variation of 
potential gradient was delayed because most of the at- 
mospheric electric observations, prior to about the year 
1915, were made near cities or at other places where 
field changes of types (a), (6), and (c) are prevalent. 
This feature, first noted by Mauchly in 1921 [6], has 
great importance for the subject. His analysis of the 
data for potential gradient over the oceans, obtained 
on Cruises IV, V, and VI of the magnetic survey yacht, 
Carnegie, showed that the diurnal variation of the gra- 
dient at sea proceeds according to universal time, not 
according to local time. 

This is illustrated by the results which are exhibited 



in Fig. 7. Average values of potential gradient, in volts 
per meter, are there plotted as ordinates against the 
hours of the Greenwich day, counting from midnight 
to midnight. The combined results for Cruises IV, V, 
and VI are showTi separately from those for Cruise VII. 
The latter, although generally of greater amplitude, 
vary in nearly the same manner as the former. If at- 
tention is fixed on either of the two lowest graphs, which 
represent hourly averages for the year, it is to be seen 
that the gradient is smallest about four hours after 
Greenwich midnight and greatest at about 19''. That 
this feature varies somewhat throughout the year is 
sho\vn by the other graphs which represent different 
quarters of the year. When these same data are aver- 
aged for hours of the local day, no significant diurnal 
variation is disclosed. Thus the change in gradient dur- 
ing the day does not depend upon daylight and dark- 
ness or other factors which vary in a manner directly 
related to the elevation of the sun at a given place. 
Another way of viewing this universal aspect is as 
follows. The negative charge of the earth as a whole in 
fair weather is greatest at about 1%^ GMT and least at 
about 4'' GMT, and the total air-earth current / varies 
in a similar manner. The latter depends partly upon the 
fact that over the oceans the diurnal variation of 
X is negligible. , 

This universal variation in potential gradient is also I 
manifested in the diurnal variation of potential gradient 
at most places on land. But factors of local origin there 
often introduce component variations which may pre- 
ponderate, especially in or near centers of population 
where the conductivity of the air is affected by atmos- 
pheric pollution. The concentration of these impurities 
is, of course, dependent not only on the rate at which 
they are supplied to the atmosphere but on the strength 
and direction of the wind, on rain, or on other processes 
which scatter these substances or carry them to or from 
the place at which the electrical features are considered. 
Variations of the content of radioactive matter in the 
air over land also result in variations of the concentra- 
tion of the small ions, upon which the conductivity of 
the air chiefly depends. Over land the air conductivity 
and the gradient may, therefore, be expected to vary 
during the day in a manner and to an extent which is 
often dependent upon a complex and variable set of 
local circumstances. 

The average potential gradient of fair weather, the 
universal diurnal variation of gradient, and doubtless 
some other temporal variations are of type (d), that is, 
they depend directly upon F, which, in turn, is pre- 
sumably dependent upon the supply current. 

The universal aspects of the electric field of the atmos- 
phere which are of chief importance may be sum- 
marized briefly as follows: (1) the electric potential 
gradient in the atmosphere during fair weather is posi- 
tive everywhere on the earth and the average value is 
about 130 V m~'; (2) the value near the equator is about 
80 per cent of the value at higher latitudes; (3) the 
gradient decreases with altitude in free air, rapidly in 
the first kilometer, then more slowly, till at an altitude 
of 10 km it is about 5 per cent of its value at the sur- 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



113 



face; (-1) the gradient at the surface varies during the 
day according to a universal routine with a minimum 
at 4*' GMT and a maximum at 19^ GMT and a diurnal 
range equal to 35 per cent of the daily mean; (5) the 
character and amplitude of this universal diurnal varia- 
tion and also the daily mean apparently vary during the 
year. Exceptions to the last two statements are con- 
spicuous at some times and places, but on a world- 
wide view the exceptions are presumably insignificant. 

THE AIR-EARTH CURRENT 

The electric current which flows from air to earth in 
fair-weather areas is predominantly an electric con- 
duction current. Although it is concei^^able that electric 
convection, as in the case of charged rain falling to 
earth, or electric displacement which depends upon the 
rate of change of electric field strength, may sometimes 
play a part in determining the electric current density 
between air and earth, yet estimates of the magnitude 
of the effects of these factors indicate that in fair 
weather they are usually small and of such character 
that they need not be considered in this brief review of 
the phenomena of atmospheric electricity. This is cor- 
roborated by several tests in which values of i deter- 
mined by the direct method were found to be about the 
same as those determined at the same place and time by 
the indirect method. The air-earth current density i is, 
therefore, essentially equal to \E, and the description 
of it is implied in the foregoing discussions of X and E. 

The average values of i derived from measurements 
over the oceans on cruises of the Carnegie are, in the 
opinion of the author, fairly representative for the earth 
as a whole. The bases for this opinion are largely as 
follows: (1) the geographical disti-ibution of these meas- 
urements is much more extensive than that for all other 
data, and (2) the data are much freer from large and 
persistent local effects than those for most land sta- 
tions. It should be noted, however, that for some land 
stations far from centers of human activity, and notably 
for those in the polar regions, the data are relatively 
free from such local effects and have about the same 
characteristics as those for the oceans. It is on this 
basis that the following statements rest. The a\^erage 
value of i derived from measurements of X and E at sea 
is about 10~^ stat amp cm~^. There is no clear evidence 
of any trend toward either a higher or a lower value in 
the 15-yr period, 1915-29, to which these data apply. 
But there is an indication that near the equator i is 
somewhat less than at higher latitudes [20]. 

The annual and the diurnal variation of i at sea have 
about the same character and relative magnitude as the 
potential gradient because only a small diurnal varia- 
tion of X is indicated by the observations and the latter 
is probably a local time effect. Also there is no definite 
evidence of an annual variation of X at sea. 

The total electric current / from air to earth for all 
fair-weather areas is i multiplied by the area of the 
earth. That the error incurred by neglecting here the 
area of thunderstorms is less than one per cent may be 
inferred from the data assembled by Brooks [8]. 

The mean value of I obtained in this way is about 



1800 amp. The error in this estimate is probably not 
greater than 10 per cent. The diurnal and possible an- 
nual variation of / are of the same character and rela- 
tive magnitude as the corresponding characteristics of 
the average for i. This total current from air to earth 
must have a counterpart which "completes the cir- 
cuit." The term "supply current" is used here to denote 
this counterpart, an elemental universal feature of at- 
mospheric electricity. Where and how is the supply 
current generated? The answer to that question has 
been sought during the last fifty years. The status of 
that search at the present time is discussed in the fol- 
lowing section. 

THE SUPPLY CURRENT AND THUNDERSTORMS 

Many proposals have been made to account for the 
fair-weather aspects of atmospheric electricity. Most 
of these were soon found to be untenable. The one sur- 
viving proposal which may give the answer as to where 
the supply current is generated is credited to C. T. R. 
Wilson. This is the suggestion that the supply current 
is generated in thunderstorms. If this is the case, the 
answer as to how it is generated doubtless must await 
the development of an acceptable theory for the genera- 
tion of electric charge in thunderstorms. This section is 
devoted to an appraisal of Wilson's suggestion. 

The universal aspects of atmospheric electricity which 
.should be recalled in this connection are, expressed in 
terms of the more comprehensive element /, as follows : 
(1) the yearly average of the total current / from air 
to earth in fair-weather areas seems to be nearly con- 
stant at a value of about 1800 amp; (2) the daily mean 
of / probably varies during the year, being greater in 
the six months from November to April than in the rest 
of the year; (3) the diurnal variation of / is such that on 
the average during the year the maximum occurs at 
about 19»> GMT and the minimum at about 4'- GMT; 
(4) the character and range of this diurnal variation 
vaiy during the year. 

The magnitude of the supply current and the charac- 
ter of its annual and diurnal variations must be the 
same as those listed here for /. Near the earth the 
supply current must flow upward, from earth to air, 
(opposite to that for /) but at some undetermined alti- 
tude, probably in the high stratosphere and below the 
ionosphere, the vertical component vanishes and the 
current is dispersed laterally. Then it returns to earth 
as an air-earth conduction current which is nearly uni- 
formly distributed over the earth. The circuit is com- 
pleted through the earth to the source, or sources, of 
the supply current, which may be located in thunder- 
storms. The fact that the air conductivity increases 
with altitude and has relatively large values at high 
altitudes seems to be of vital importance for the exist- 
ence of such an electric circuit. 

The first evidence in favor of Wilson's suggestion that 
the supply current is generated in thunderstorms was 
obtained in an analysis, made by Whipple [22], of the 
thunderstorm data for the world, assembled by Brooks 
[8]. That investigation indicates that thunderstorm ac- 
tivity, for the earth as a whole, varies during the Green- 



114 



ATMOSPHERIC ELECTRICITY 



wich day in the same manner as does the air-earth cur- 
rent of fair weather. This evidence is exhibited in Fig. 8, 
where the ordinates represent the area over which land 
thunderstorms are in progress at the time of the Green- 
wich day denoted by the abscissae. By comparing this 
graph with either of the lowest graphs for potential 
gradient in Fig. 7, a remarkable similarity will be noted. 
Whipple also concludes that the character of the diurnal 
variation changes during the year in about the same 
manner for the two phenomena. This result indicates 
that if the net current generated in the representative 
thunderstorm is directed upward from the earth to the 
high atmosphere, and if the total current from all 
storms is great enough (average 1800 amp), the supply 
current would satisfy the requirements listed above. It 
is surprising, in view of the character of the data and 
their scantiness for large areas of the earth, that this 
result could be obtained. Whipple apparently used 
satisfactory methods in his analysis. Maybe this result 
indicates that thunderstorms over the oceans and in 
sparsely settled regions of the earth do not contribute 
much to the supply current. 



g 120 

°: 100 

< 80 

Ui 

o: 

< 60 

i 40 
£ 20 






4 6 8 10 12 14 16 18 
GREENWICH MERIDIAN TIME 



20 22 24 



Fig. 8. — Diurnal variation in prevalence of thunderstorms. 
The ordinate is the estimate of the average area of land- 
thunderstorms in progress on the whole earth. {After F. J . W. 
Whipple and F. J . Scrase.) 

Other methods should be used to check Whipple's 
results. It seems that it may be practicable now by the 
use of suitably designed atmospheric recorders at a com- 
paratively small number of well-distributed stations to 
make a complete "sweep" of the earth and with satis- 
factory registration for one year to obtain the required 
data. From such data one would hope to derive a 
record of lightning frequency as a function of Green- 
wich time which may be more suitable information for 
this purpose than records of thunderstorm occurrence. 

Although Whipple's results seem to show that if 
thunderstorms are the seat of the supply current, the 
diurnal and annual variation of that current would each 
be of the right type, it is yet to be ascertained whether 
the thunderstorms do contribute a current of the right 
sign and magnitude to the circuit previously described. 
In principle this may be ascertained either by making 
measurements of the required elements at the earth's 
surface beneath storms or by making the proper survey 
over the top. 

No adequate survey beneath a thunderstorm has ever 
been made. However, T. W. Wormel made part of the 



required measurements at Cambridge, England, which 
he used together with data obtained elsewhere by other 
observers to draw up a balance sheet of the quantity 
of electricity lost and gained by 1 km^ in a year. 
Wormel's balance sheet is as follows: 

Negative charge gained Coulombs km~* yr~ 

1. By natural point discharge 

2. By lightning discharge 
Total negative charge gained 

Positive charge gained 

3. By atmospheric conduction 

4. By precipitation 
Total positive charge gained 

Net gain, negative charge 



Coulombs km 
100 
20 
120 

60 
20 
80 
40 



Although it is interesting to see what comes from an 
attempt to strike such a balance it may not have much 
significance for the problem at hand. Item 3 is the best- 
determined one, but Wormel uses the small value ob- 
tained at a few places in England whereas the electric 
surveys of the Department of Terrestrial Magnetism, 
Carnegie Institution of Washington, indicate a value 
almost twice this for representative areas of the earth. 
The interpretation of the data from which Item 1 was 
obtained may be questioned and, furthermore, it cer- 
tainly is much too large for vast areas of the earth — 
especially the oceans and the polar regions. In addition 
to questioning whether Items 2 and 4 are representative 
it should be noted that uncertain elements enter into 
their estimation. This approach to the problem seemed 
so difficult that another way was sought. 

Surveys of the electric current density over the tops 
of thunderheads seemed to the author to be feasible 
when in 1946 pressurized aircraft became available for 
use in scientific projects. Owing to the absence of pre- 
cipitation and the rarity of lightning in the clear air 
above a thunderhead, electric circumstances there are 
simpler than beneath the storm. This was the basis for 
expecting that the transfer of electricity in the air above 
the storm occurs chiefly by electric conduction and that, 
as a consequence, measurements of the vertical com- 
ponent of the electric current density made at short 
intervals (2 sec) on a number of traverses over a 
storm would constitute an adequate basis for estimating 
the magnitude and direction of the total current from 
a storm. Surveys of this sort were made in 1947 and 
1948, as a joint project of the Department of Terrestrial 
Magnetism, Carnegie Institution, and the U. S. Air 
Force. A technical report is being prepared by O. H. 
Gish and G. R. Wait.^ 

Successful surveys of twenty-four storms were made. 
In these storms the current was directed upward, that 
is, positive charge was transferred upward. This is 
favorable to Wilson's suggestion. The magnitude of the 
current ranged from zero to 6.5 amp. The average cur- 
rent for all storms was 0.6 amp, and that for all except 
the one unusually large value, was 0.3 amp. 

Is an average current per thunderstorm cell of 0.3 to 
0.6 amp adequate to satisfy the requirement that the 
total supply current be 1800 amp? It would be, if the 

5. See "Thunderstorms and the Earth's General Electrifica- 
tion," by O. H. Gish and G. R. Wait, /. geophys. Res. 55: 473- 
484 (1950). 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



115 



average number of thiinderstoiin cells or centers of 
electric activity in progress on the earth were between 
3000 to 6000. This is several times Brooks' estimate of 
1800. The latter estimate is, however, not apphcable 
here for the following reasons. The data used by Brooks 
consisted of reports of thundery days — days on which 
thunder was heard — and there is no indication that he 
took into account the fact that at some places two, and 
occasionally more, visually distinct thunderstorms oc- 
cur within hearing distance of a station on the same 
day. Neither was it considered that in a given thunder- 
storm there are sometimes several well-separated cen- 
ters of electrical activity in progress simultaneously. 
These considerations indicate that a world population 
of between 3000 and 6000 centers of electrical activity 
may be admissible, and, that the answer to the fore- 
going question is "Probably, yes." 

This provisional answer is, however, subject to an- 
other condition, namely, that the values for total cur- 
rent obtained from these surveys may be too large 
because part of the current, represented by the measure- 
ments, may flow in a local circuit either to the lower 
pole of the cloud or to bound charge on the earth in the 
vicinity of the storm. An adequate evaluation of this 
effect has not yet been completed. Until this is done 
and until a more reliable estimate can be made of the 
world population of centers of electric activity, one can 
say only that the available evidence is favorable for the 
view that the supply current is generated in the 
thunderstorms, but much more investigation is re- 
quired in order to reach a definite and reliable conclu- 
sion. This theory has at the present time no serious 
rival. No other theory known to the author has the 
potentiality of accounting for the universal, diurnal, 
and annual variation of /. 

An interesting corollary of this theory is that if the 
supply current originates in thunderstorms, the uni- 
versal, diurnal, and other variations may be regarded 
as a measure of the thunderstorm activity of the whole 
earth. It accordingly seems likely that the record of i 
at a station where local disturbances are small would 
constitute an approximate record of the thunderstorm 
activity of the earth, showing how it varies from day to 
day and perhaps even from hour to hour. Small local 
effects are more likely to obscure the latter than the 
former. Such effects could, however, doubtless be largely 
eliminated from the data if i were registered at a 
moderate number of suitably selected stations. Such 
records might be valuable in the study of some prob- 
lems of world meteorology. For example, they might 
provide answers to questions such as, Does world 
thunderstorm activity vary from year to year and is it 
correlated with sunspot activity? The data now avail- 
able for i apparently point toward a negative answer 
to these questions. 

How is the supply current generated? How are the 
electric charge-clouds of thunderstorms developed? 
These are two questions which doubtless have a single 
answer, provided that the supply current is generated 
in thunderstorms. In the author's opinion, no adequate 
answer to these questions has yet been published. Be- 



cause of this circumstance the discussion which follows 
is limited to an outline of important aspects of the 
theories which have been proposed, the chief electrical 
features which must be accounted for, and some other 
conditions which must be satisfied. 

The electrical cycle of a thunderstorm may be re- 
garded as consisting of the following parts: (1) an initial 
separation of charge, a small-scale phenomenon in which 
some particles of precipitation become charged with 
electricity of one sign and the adjacent air, or some of 
the smaller particles, becomes charged with the other 
sign, (2) a large-scale separation of charge, possibly 
occurring in several steps, by which large charge-clouds 
of several cubic kilometers in volume are formed at 
more or less definite levels in the thundercloud, (3) the 
initiation of discharge from a cloud, namely, the mo- 
bilization of the charges residing on particles widely dis- 
tributed throughout the charge-cloud, thus preparing for 
the succeeding steps which constitute (4) the lightning 
discharge. 

The last of these, the lightning discharge, has been 
comparatively well elucidated in recent years. It is the 
subject of a separate article in this Compendium^ and 
will not be discussed here. 

Ivnowledge regarding the other steps, however, is in 
an unsatisfactory state. More factual evidence is re- 
quired before theories of these aspects of the electric 
cycle of the thunderstorm can be securely established. 

The initiation of a lightning discharge — the getting 
together of the charges which are widely distributed on 
ice particles or raindrops or both — although one of the 
unexplained aspects of the thunderstorm has little rele- 
vance to the development of the charge-cloud, and will 
be dismissed with the statement that the glow dis- 
charge, which starts at the surface of charged particles, 
is presumably involved. When the glow discharge 
spreads throughout a sufficient volume of the charge- 
cloud, the discrete charges on the particles are mobil- 
ized for the lightning discharge. However, there is little 
direct evidence to support this surmise. 

The electric structure of the thunderstorm is often so 
complex that exact descriptions, such as could be made 
with the aid of general harmonic analysis when ade- 
quate data are available, have not been undertaken. 
One might say, however, that in the classical work of 
C. T. R. Wilson a fair estimate of the principal moment 
was obtained. An advance beyond this was realized in 
the work of Workman, Holzer, and associates [23]. The 
results of these and other investigators are in fair agree- 
ment on the gross aspects of the electric charge-clouds. 
These and some other features which bear on the later 
discussion are listed here. 

1 . There are two principal charge-clouds in the typi- 
cal thunderstorm. The positive cloud is usually located 
at an altitude greater than that of the negative cloud. 
An altitude of 6 to 7 km for the former and of 3 to 4 
km for the latter has been estimated. 

2. Charge-clouds tend to be cumuliform rather than 
stratiform. 



6. Consult "The Lightning Discharge" by J. H. Hagenguth, 
pp. 136-143. 



116 



ATMOSPHERIC ELECTRICITY 



3. The size of a charge-cloud which has developed to 
the stage where lightning of average intensity may oc- 
cur is comparable to that of a sphere of at least 1-km 
diameter and probably is several times that dimension. 
For a cloud of smaller size, having a charge of 20 
coulombs, the dielectric strength would be exceeded in 
air containing water drops, ice pellets, or crystals. 

4. The region of primary electrical activity (loca- 
tion uncertain) where the initial charge separation and 
the large-scale separation occur jointly, doubtless has a 
cross section less than that of the charge-clouds. 

5. The average cloud charge developed between 
lightning flashes is 20 to 30 coulombs. 

6. The average rate of regeneration for charge-clouds, 
after lightning discharges, is about 4 amp but values as 
great as 20 amp are sometimes indicated. In regenera- 
tion the charge approaches an equilibrium value in 
approximately an exponential manner. One may ac- 
cordingly speak of a relaxation time. An average value 
of the latter is about 5 sec. The relatively small depar- 
ture of individual values from this average seems to 
have some significance. 

7. No convincing evidence has been found of ab- 
normally large electrical conductiAdty of the air above 
thunderclouds or under thunderclouds at the earth's 
surface. 

These items will be referred to by number in later 
paragraphs. 

The initial separation of charge has been attributed to 
various processes: The disruption of drops of pure water 
will effect a separation of electric charge with positive 
charge on the drops and negative charge in the air (a 
few thousandths of one per cent of some salts as an 
impurity annuls this effect). G. C. Simpson developed 
a theory which depended on this process. This theory 
was in vogue for more than a decade, but it became 
untenable when it was found that the positive charge- 
cloud is usually above the negative cloud. 

Ion-capture is the fundamental process in a theory 
developed by C. T. R. Wilson. This process may be 
illustrated as follows. A water drop located in the nor- 
mal electric field will have a positive charge induced on 
its lower surface and a negative charge on its upper 
surface. If the atmosphere contains ions (large ions as- 
sumed by Wilson) , the positive ions will drift downward 
and the negative ions upward both with a velocity 
much less than that of the falling drop. The negative 
ions will be attracted by the positive charge on the 
bottom of the drop and those located in or near the 
path of the drop will be captured. The positive ions, 
however, will be repelled by the charge on the bottom 
of the drop and escape capture because when such an 
ion is in position to be attracted by the negative charge 
on the top of the drop, that attraction is not great 
enough to effect a capture. In this way larger drops may 
acquire a net negative charge. The larger drops with 
their negative charge will accumulate in the lower part 
of the thundercloud while positive charge, without in- 
volving the ion-capture process, will accumulate at a 
higher level. This is a favorable aspect of Wilson's 
theory, since it is in accord with the observed orienta- 



tion of the principal charge-clouds. Although there are 
reasons for thinking that pellets or crystals of ice may 
also capture ions in this way, this requires more in- 
vestigation if the ion-capture process is to be considered 
active in the region of sub-zero (centigrade) tempera- 
ture where the principal charge-clouds are found. This 
ion-capture process requires that a relatively large con- 
centration of ions, preferably of low mobility, obtains 
in the electrically active part of a storm cloud. Such a 
condition has not yet been observed, except as a local 
phenomenon of relatively rare occurrence, namely at 
times when glow or brush discharge (St. Elmo's fire) 
occurs. Unless there is some potent source of such ions 
other than the glow or spark discharge, Wilson's ion- 
capture process can act only in a secondary role after 
fields capable of initiating glow discharge have been 
developed by another mechanism. 

The collision of ice particles has been suggested as a 
process for the initial charge separation. Charge de- 
veloped by drifting snow (positive in the air) is more 
conspicuous than that for splashing rain but it is doubt- 
ful whether this process is effective in the atmosphere 
remote from the earth's surface. 

Evaporation, condensation, and sublimation acting 
singly or in combination have been assumed as primary 
processes [11, 16]. Findeisen's experiments [11] indi- 
cated that these processes are much less effective than 
is the process which is involved in the formation of sleet 
{Vergrawpelung). Dinger and Gunn [9] found an effect 
associated with the freezing of water and the melting of 
ice. Gunn [16] also assumed that a raindrop is essen- 
tially a concentration cell, and he indicated how it may 
acquire a net negative charge during condensation and 
a net positive charge during evaporation. Frenkel [13] 
developed a theory in which the electrokinetic potential 
of a raindrop, or cloud droplet, was proposed as the 
basis for the initial separation of charge. The funda- 
mental element of this theory is similar to that of 
Gunn's theory. 

A very active process of charge separation was dis- 
covered by Workman and Reynolds [24]. This occurs 
during orderly freezing of water in which very small 
quantities of certain salts are dissolved. The effective- 
ness and the direction of the process depend upon the 
concentration and nature of the solute. In most solu- 
tions for which a pronounced effect was reported, nega- 
tive ions are captured by the ice. A prominent exception 
to this was found in solutions of the ammonium salts 
for which the solid phase acquires a positive charge. 

The charge developed by this process in the freezing 
of one cubic centimeter of water is extraordinarily large 
for a number of solutions which were examined. For 
solutions of NaCl the greatest effect was for an 0.83 
X lO"* normal concentration. This gave a charge of 
9.2 X 10* stat coulombs from the freezing of one cubic 
centimeter of solution. The solid phase acquired a nega- 
tive and the liquid phase a positive charge. The largest 
value reported was for a CsF solution of 11.1 X lO""* 
normal concentration. This is 44 X 10'' stat coulombs 
cm~^ These values are of a much greater order of mag- 
nitude than the largest value reported by Lenard and 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



117 



associates for the violent disruption of a water drop, the 
latter being about 2 stat coulombs for each cubic centi- 
meter of water that is invoh'ed. Perhaps the results re- 
poi-ted by Findeisen and by Dinger and Gunn are in 
part attrilnitable to the orderly freezing of wate-. 

Other in\'estigations of Workman and Reynolds indi- 
cate that cloud droplets may contain solutes of the 
right type and in suitable concentration for this process 
to occur in the atmosphere. Favorable results were also 
obtained in an experiment designed to imitate the 
growth of hail. 

The advantage which derives from the relatively 
large amount of electric charge separated in the orderly 
freezing of suitable solutions may be illustrated by the 
following simple calculation. If the amount of charge 
separated in the formation of one gram of hail or sleet 
is 10* stat coulombs (about 2 per cent of the largest 
value reported), then in order that the rate of charge 
regeneration of a charge-cloud be 4 amp, or 1.2 X 10'° 
stat amp (Item 6, of the foregoing list), it is necessary 
that at least 1 .2 X 10'' g (about one short ton) of hail be 
formed each second in the region of primary electrical 
activity. In contrast to this, the mass of water drops 
that would have to be violently disrupted each second, 
if the breaking-drop process were the basic factor, 
would be at least 6 X 10° g or more than 6500 short 
tons. This apparently shows that the breaking-drop 
process is not adequately active, but that generation of 
charge by orderly freezing may be sufficiently active 
provided that, among other conditions already indi- 
cated, hail is always a large constituent of the hydro- 
meteors in a typical thunderstorm. 

None of the other primary processes so far proposed 
has yet been shown to have the generating capacity re- 
quired. Acceptance or rejection of either Gunn's or 
Frenkel's theory depends on whether or not the re- 
laxation time of the process is adequate, that is whether 
l/(47rX) in the region of primary activity, is, on the 
average, about 5 sec (Item 6). This is equivalent to 
saying that these theories are not acceptable unless the 
air conductivity in the region of primary activity is at 
least ten times that for normal air at an altitude of 5 
km. At present it seems unlikely to the author that this 
condition is satisfied, but since this opinion is based 
chiefly on indirect evidence, more direct exploration in 
the future may bring forth evidence which contradicts 
this view. 

The ion-capture process which is elemental in C. T. 
R. Wilson's theory also postulates that a relatively high 
concentration of ions prevails in the region of primary 
activity, where the initial separation of chai'ge occiu's. 
Since these ions are assumed to have a very small mo- 
bility, it seems likely that the air conductivity would be 
abnormally small in some parts of the cloud. This postu- 
late cannot be definitely refuted by evidence now avail- 
able. 

The large-scale separation of charge which follows 
the initial step in charge generation must also proceed 
at the rate of 4 amp for each typical center of electrical 
activity. In all theories mentioned in this article it is 
postulated (1) that after the initial step the larger drops, 



or particles of precipitation, tend to have an electric 
charge of sign opposite to that of very small particles or 
of air ions, and (2) that, principally under the action of 
gravity, large particles fall away from the small ones at 
a velocity v which is equal to the difference in the ter- 
minal velocities. 

Although there are no obvious alternatives to these 
postulates, there seems to be some ground for doubting 
whether the second is acceptable. This is illustrated in 
the following paragraph. 

Let p denote the total net charge on the large par- 
ticles in a cubic centimeter of air; v, the average velocity 
of these particles relative to the .smaller ones; and A, 
the cross-sectional area, nonnal to the direction of v, of 
the region of charge separation. The total current /' 
from large-scale separation then is I' = pvA. Now in 
order that the value of /' may be 4 amp, pvA must 
equal 1.2 X 10'° stat amp. The space charge p is 
limited by several circumstances. One which is amenable 
to simple treatment is that for no considerable propor- 
tion of the drops or particles shall the charge q of each 
drop of radius r be greater than lOOr-. Larger values 
lead to electrical discharge. If there are n drops in each 
cubic centimeter, all of the same size and same charge, 
the maximum admis.sible space charge is p,„ ^ lOOnr^. 

The mass of drops m in 1 cm^ of air is also limited, 
and in terms of this m, the foregoing expression for the 
upper limit of p maj^ be written p,„ ^ 300?n/(47rr). 
Now V is an increasing function of r, but in such a way 
that p,„y decreases with an increase of r if m is constant. 
For a veiy large value of m, namely, 5 X 10~^ g cm~^ 
p„v is 0.25 for hailstones having a diameter of 3 cm, 
and is 1.1 for droplets of 0.4-mm diameter. If the inter- 
mediate value 0.5 for p,„v is used, one finds that A ^ 
2.4 km^. Such a value for A is of satisfactory magnitude, 
but in view of the assumptions made hei'e this estimate 
is doubtless much smaller than is actually required. It 
seems unlikely that in nature a large proportion of the 
precipitation particles are highly charged at a given 
time, and it is also doubtful whether such a large con- 
centration of water, in either the liquid or the solid 
phase, occurs in a typical thunderstorm. The effect of 
the electric field, which tends to reduce v, especially if 
the pai-ticles are small, is also not considered here. Be- 
cau.se of these and other considerations it seems evident 
that the value required for A is much larger than 2 or 
3 km^. But if this conclusion is correct, that would en- 
tail the difficulty of accounting for the size, .structure, 
and orientation of the charge-clouds — features which 
are, at least roughly, indicated by measurements of the 
electric field above thundci-clouds, within them, and 
below them at the earth's surface. 

The object of the foregoing statement is to indicate 
how unsatisfactory is the present status of theories re- 
garding the large-scale separation of charge in thunder- 
storms. No theory is yet secure if settling under the 
action of gravity is assumed to be essential in the large- 
scale .separation of charge. If observations eventually 
show that the concentration of water in the typical 
thunderstorm is considerably greater than 5 g m^', at 
least in the region of primary electrical activity, this 



118 



ATMOSPHERIC ELECTRICITY 



difficulty might be removed. But it may be that some 
force other than gravity effects the separation of the 
larger from the smaller charged particles. A combina- 
tion of centrifugal action and straight wind has been 
suggested, but it is not yet evident that the wind struc- 
ture of the thundercloud is suitable for this. 

This discussion of selected electric features of 
thunderstorms and of theories which have been pro- 
posed to account for those features was designed to 
show that at the present time there are only a few clues 
as to how the charge-clouds are developed. One of these 
is the recent discovery that the orderly freezing of very 
dilute solutions of certain salts is a very effective process 
for the initial step in the generation of electric charge. 
The potency of this process is such that if conditions in 
the thunderstorm are favorable, the charge on the pre- 
cipitation particles may be maintained at a value so 
near the maximum, limited by electric breakdown, that 
the prospects of accounting for the large-scale separa- 
tion of charge will be improved. More observations of 
electrical and other conditions, especially within 
thunderstorms, and more carefully controlled specula- 
tion are required to find the answer to the question. How 
are the charge-clouds in thunderstorms developed? 

Until the foregoing question is answered, the added 
question, How is the supply current generated? will 
probably also remain unanswered. This statement de- 
pends upon the fact that with the evidence now at hand 
one may entertain the view that the supply current is 
generated in the thunderstorms of the earth. Before this 
view was advocated, the fair-weather aspects of atmos- 
pheric electricity and thunderstorm electricity were 
regarded as unrelated geophysical phenomena. Now, 
since it seems likely that the universal aspects of at- 
mospheric electricity derive from thunderstorms, a more 
unified exposition of the subject is feasible. 

From a remote position in space an ideal observer, 
whose acute vision could encompass the whole earth, 
might see in the broad prospect of atmospheric electric 
phenomena the following features: first, the numerous 
thunderstorms in progress on the earth — usually several 
thousand of them. He would notice that they are very 
scarce in the polar regions and especially abundant in 
the afternoon on land areas in middle and low lati- 
tudes. If each hour throughout a year he should count 
the total number of electric storm centers, he would 
probably note that, on the average, the count tends to 
be greatest for the hour when it is mid-afternoon at 
about longitude 75 °W and least for the hour when it is 
mid-afternoon at about longitude 150°E. Other varia- 
tions in the count would doubtless also be found. 

If this observer had a special sense with which he 
could "see" a flux of electricity, he would not only 
notice the lightning flashes in and about the electric 
storm centers, but would also see a complicated pattern 
of electric flux in, about, and beneath each electric 
storm center. But the most alluring feature would be a 
narrow stream of the electric effluvium which emerges 
from the top of the upper charge-cloud, flows upward 
and along its course, widens and becomes less dense 
until it merges at a high level with similar streams from 



the other storms to form a world-wide ocean of electric 
effluvium. From this ocean a much more tenuous but 
nearly uniform electric flux could be seen to proceed 
downward to the earth eveiywhere except in and about 
electric storms. The circuit continues through the earth 
and back to the storm centers. The density of this 
universal flux from air to earth would be seen to vary 
during the day, from day to day, and during the year, 
in about the same manner as does the corresponding 
count of storms. But apparently it varies little, if at all, 
from year to year. 

This is an impressionistic sketch of the broad prospect 
of atmospheric electricity as it is seen by the author in 
the light of evidence now available. 

OUTSTANDING PROBLEMS 

In the broadest sense there are two main problems in 
the field of atmospheric electricity: 

1. To locate the source of those universal aspects 
which are epitomized in the concept, supply current. 

2. To elucidate the mechanism which generates the 
supply current. If, as now seems likely, the supply cur- 
rent is generated in thunderstorms, the last-mentioned 
problem and that posed by the electric aspects of the 
thunderstorm have much in common. 

It is of course necessary to have an adequate quanti- 
tative description of the phenomena before the rationale 
of the subject is developed. In this respect there are 
many minor and some major inadequacies. Some of the ,i 
more important observations required in order to fill ! 
this need are: 1 

1. Measurements of air conductivity in the high at- : 
mosphere, especially in the altitude range 18 km to 60 I 
km. New techniques would be required to make the i 
measurements in the upper part of this region. 

2. Measurements of air conductivity, and counts of 
Aitken nuclei in thunderstorms. These items are sug- 
gested, rather than measurements of small-ion and 
large-ion concentrations, because measurement of the 
latter elements is more difficult. The technical difficul- 
ties of making reliable measurements of air conductivity 
from aircraft, during flight through clouds, have not 
yet been overcome. 

3. More extensive, or more comprehensive, informa- 
tion about the population of the electric storm centers 
that are in progress on the earth. Until this information 
is available, no reliable estimate can be made of the 
average current which a typical electrical storm center 
must contribute to the make-up of the supply current. 
It is desirable that data be collected to verify, or to 
refute, the diurnal variation in storm population re- 
ported by Whipple. Perhaps this could be done by radio 
methods used for measuring atmospherics and "back- 
ground noise," with some modification to adapt them 
for use in a world survey of electric storm activity. 
Apparently it would be necessary to make such meas- 
urements at a relatively small number of well-distrib- 
uted stations. 

4. More data for the air-earth current density i or 
for the elements X and E, in order to ascertain whether, 
and in what manner, the supply current varies during 



UNIVERSAL ASPECTS OF ATMOSPHERIC ELECTRICITY 



119 



the jrear. The evidence now at hand is inadequate for a 
rehiible determination of even the quahtative aspects of 
this feature. Except for measurements made on the 
cruises of the Carnegie, data for i have been obtained at 
only a few places. 

5. Information which will help better to ascertain 
the electric structure of the thunderstorm. More meas- 
urements of electric field in the vicinity of thunder- 
storms (made simultaneously at a number of stations) 
are required for more types of storms. More measure- 
ments, made within storms, of the electric charge dis- 
tribution are desirable. 

6. More determinations of the rate of regeneration of 
charge, after a lightning discharge. Although the data 
now at hand appear to be comparatively reliable, they 
should be checked because they set a requirement which 
may not be satisfied by any theory which depends upon 
the force of gravity for the large-scale separation of 
charge. 

7. Determination of which of the various known 
processes of initial charge separation occur in a thunder- 
storm. It will doubtless be difficult to find a definite 
answer to this, but the answer should be sought. 

8. Information on how the widely scattered discrete 
charges in a charge-cloud are mobilized for the lightning 
discharge. This is another question for which a more 
definite answer is awaited. 

These are some of the matters in atmospheric elec- 
tricity which deserve attention. Others have been in- 
dicated in the body of this article. 

REFERENCES 

This brief list of treatises and papers is designed chiefly to 
serve as a guide for the reader or investigator who desires to 
read more comprehensive discussions of the subject. Technical 
articles which contain good bibliographies have been given 
preference. These citations, however, should not be used as a 
basis for assigning priority of or credit for discovery. 

I. Treatises. 

1. Fleming, J. A., ed.. Terrestrial Magnetism and Electricity. 

New Yorlc, McGraw, 1939. Reprinted with corrections: 
New York, Dover Publications, 1949. The following chap- 
ters bear on atmospheric electricity: 

GiSH, O. H., "Atmospheric Electricitj'," Chap. IV. 

ToHRESON, O. W., "Instruments Used in Observations of 
Atmospheric Electricity," Chap. V. 

Beekneh, L. v., "Radio Exploration of the Earth's Outer 
Atmosphere," Chap. IX. 

ScHONLAND, B. F. J., "Thunder-Clouds, Shower-Clouds 
and Their Electrical Effects," Chap. XII. 

Harkadon, H. D., "Bibliographical Notes and Selected 
References," Chap. XIII. This bibliography contains 
references to other general treatises and to many techni- 
cal papers published prior to 1939. 

II. Treatises Published since 1939. 

2. Chalmers, J. A., Atmospheric Electricity. New York, 

Oxford, 1949. 



3. Israel, H., Das Gewitter. Leipzig, Akad. Verlagsges., 1950. 

4. Maurain, C, La Foudre. Paris, A. Colin, 1948. 

5. MiTRA, S. K., The Upper Atmosphere. Calcutta, The Royal 

Asiatic Society of Bengal, 1948. 

III. Technical Papers and Reviews. 

6. Ault, J. P., and Mauchly, S. J., "Ocean Magnetic and 

Electric Observations Obtained aboard the Carnegie, 
1915-21." Res. Dept. Terr. Magn., Carneg. Inst. Wash. 
Publ. No. 175, 5: 197-286 (1926). 

7. Bricard, J., "L'Equilibre ionique de la basse atmosphere." 

J. geophys. Res., 54: 39-52 (1949). 

8. Brooks, C. E. P., "The Distribution of Thunderstorms 

over the Globe." Geophys. Mem., 3: 145-164 (1925). 

9. Dinger J. E. and Gunn, R., "Electrical Effects Asso- 

ciated with a Change of State of Water. Terr. Magn. 
atmos. Elect., 51: 477-494 (1946). 

10. EvERLiNG, E., und Wigand, A., "Spannungsgefalle und 

vertikaler Leitungsstrom in der freien Atmosphare, nach 
Messungen bei Hochfahrten im Freiballon." Ann. 
Physik., 66: 261-282 (1921). 

11. FiNDEisEN, W., "Uber die Entstehung der Gewitterelek- 

trizitat." Meteor. Z., 57: 201-215 (1940). 

12. FoRBUSH, S. E., Stinchcomb, T. B., and Schein, M,, "The 

Extraordinary Increase of Cosmic-Ray Intensity on 
November 19, 1949." Phys. Rev., 79: 501-504 (1950). 

13. Frenkel, J., "A Theorj- of the Fundamental Phenomena 

of Atmospheric Electricity." J. Phys. {U.S.S.R.), 8: 
285-304 (1944). 

14. GisH, O. H., and Sherman, K. L., "Electrical Conductiv- 

ity of Air to an Altitude of 22 km." Nat. Geogr. Sac. 
Contrib. Tech. Papers, Stratosphere Ser., No. 2, pp. 94- 
116 (1936). 

15. Ionic Equilibrium in the Troposphere and Lower Stra- 
tosphere. Internat. Assoc. Terr. Magn. Elect., Washing- 
ton Assembly, Sept., 1939. 

16. Gunn, R., "The Electricity of Rain and Thunderstorms." 

Terr. Magn. atmos. Elect., 40: 79-106 (1935). 

17. Schweidler, E., Luftelektrizildt. Einfiihrung in die Geo- 

physik, Bd. II. Berlin, J. Springer, 1929. (See pp. 291- 
375) 

18. Die Aufrechterhaltung der elektrischen Ladung der 

Erde. Hamburg, H. Grand, 1932. 

19. ScRASE, F. J., "The Air-Earth Current at Kew Observa- 

tory." Geophys. Mem., Vol. 7, No. 58 (1933). 

20. ToRREsoN, O. W., and others, "Scientific Results of Cruise 

VII of the Carnegie during 1928-1929. Oceanography, III, 
Ocean Atmospheric-Electric Results." Carneg. Instn. 
Wash. Publ., No. 568 (1946). 

21. Wait, G. R., "Atmospheric-Electric Results from Simul- 

taneous Observations over the Ocean and at Watheroo, 
Western Australia." Trans. Amer. geophys. Un., 23: 304- 
308 (1942). 

22. Whipple, F. J. W., "Modern Views on Atmospheric Elec- 

tricity." Quart. J. R. meteor. Soc, 64: 199-213 (1938). 

23. Workman, E. J., Holzer, R. E., and Pelsor, G. T., "The 

Electrical Structure of Thunderstorms." Tech. Notes riat. 
adv. Comm. Aero., Wash., No. 864 (1942). 

24. Workman, E. J., and Reynolds, S. E., Thunderstorm 

Electricity. Final Rep., Signal Corps Res. Contract No. 
W-36-039SC-32286, Sept. 30, 1948. (See p. 26) 



IONS IN THE ATMOSPHERE 

By G. R. WAIT 

Carnegie Institution of Washington 

and W. D. PARKINSON 

Johns Hopkins University 



In considering the subject of atmospheric ions, it has 
been possible, because of space hmitations, to consider 
only those conditions of the atmosphere which are 
regarded as normal and to include in the discussions, 
which are of necessity brief, only those items which are 
most important. References to investigations have also 
been restricted to those regarded as most pertinent to 
the subject at hand. 

It has been known since late in the eighteenth cen- 
tury that an insulated charged body left in the air will 
slowly lose its charge by a process other than leakage 
across the supporting insulators. This process of gaseous 
conduction of electricity was interpreted by J. J. Thom- 
son [42] as due to the presence in the gas of charged 
particles which, by analogy with the conduction in 
electrolytes, were called "ions." 

The concentration of ions in the atmosphere is meas- 
ured by an instrument called an ion counter. In principle 
the instrument is simply a charged cylindrical condenser 
through which air is drawn at a known velocity. The 
rate at which the charge on the central electrode changes 
provides a measure of the number of ions in the air 
stream and consequently the ion concentration of the 
air. If the voltage between the electrodes is sufficientlj^ 
high, all ions from the air stream will be collected. 
Normally this voltage difference is selected so as to 
collect all ions of a particular mobility group and as few 
as possible of the less mobile ions. If a measure of the 
concentration of a lower-mobility group is desired, 
interference from ions of higher mobility may be avoided 
by first passing the air through another cylindrical 
condenser operated with sufficient voltage to remove the 
more mobile ions but only a small proportion of those 
to be measured. The theory and operating details of 
ion counters are discussed in special articles and texts 
on the subject [6, pp. 252-258; 10, 28, 41]. 

Ionic Mobilities 

An electron is released in the formation of a pair of 
small ions, but remains free for only a short time. The 
fact that no high-mobility group of negative ions is 
found shows that very few free electrons are present in 
the lower atmosphere. Small ions of the atmosphere 
have an average life of the order of a minute, so they 
are thoroughly aged during most of their lives, and are 
subject to the influences of many atmospheric constitu- 
ents existing in minute quantities. According to the 
picture recently given by Overhauser [34], an atmos- 
pheric small ion can be imagined as a charged molecule 



which is continually associating with, and dissociating 
from, one or more other molecules. The time a certain 
type of molecule remains associated with an ion depends 
on its electrical properties. 

The average velocity with which an ion drifts through 
a gas under the influence of an electric field is propor- 
tional to the strength of the field. The ratio of the 
velocity to the field strength is called the mobility of the 
ion. The unit of measurement (referred to hereafter as 
centimeters) is centimeters per second per volt per 
centimeter. 

Numerous mobility measurements on gaseous ions 
have been made in the laboratory [22]. The value of the 
mobility is found to depend upon both the ion and the 
gas through which it moves. It also is affected by the 
presence of very slight traces of water vapor and other 
impurities. The ion can apparently become attached to, 
or lose its charge to, an impurity molecule. Some molec- 
ular impurities are known to associate readily with a 
positive ion, some with a negative ion, and some with 
either. In most laboratory measurements, an effort 
is made to remove all traces of water vapor or other 
impurities so the values may be representative of the 
gas. For freshly formed positive and negative ions in 
air, Erikson [5] obtained a value for the mobility of 
1.87 cm. In a few hundredths of a second the positive- 
ion mobility had decreased to 1..36 cm, due, he believed, 
to the ion becoming attached to a neutral air molecule. 
Bradbury [3] obtained what he considered a more 
representative value for each sign after taking extreme 
precautions to remove practically all traces of impur- 
ities. Values obtained by him were 2.21 and 1.60 cm 
as the negative and positive ion mobilities, respectively. 

This requirement for such a high degree of purity for 
the air in mobility determinations leads one to question 
the extent to which laboratory-determined values can 
be accepted as the values of the small-ion mobilities in 
atmospheric electric work. 

Mobility determinations of the small ions in the 
atmosphere have been made by various methods. Prob- 
ably the method most frequently used is the ratio of air 
conductivity to small-ion content. This will not result 
in high precision unless proper precautions are taken to 
eliminate various errors which can easily enter and 
unless a correction is made for the lower-mobility ions 
caught by the ion counter. 

The published values [14] of mobilities of small ions 
in the atmosphere, from measurements made many 
years ago, show a great deal of scatter. There are reasons 



120 



IONS IN THE ATMOSPHERE 



121 



for believing that in man.y of these detei'minations the 
precision was not especially high, and in some cases it 
seems probable that considerable error resulted from 
the collection of lower-mobility ions by the ion counter 
(resulting in too low a value for the mobility). The 
latter was probable because at one time it was custom- 
ai-y to apply to the ion counter a rather high potential, 
frequently as much as several times that reciuired for 
small-ion saturation. A list of a few mobility values in 
air, from measurements where it is known that precau- 
tions were taken to avoid various possible errors, is 
given in Table I. The several values are in quite good 

Table I. Some Mobility Values for Small Ions 



Refer- 


Station 


Period 


Mobility in cm 
sec-Vvolt cm'' 




k+ 


k- 


44] 
39] 
14 
29 


Carnegie, Cruise VII 
College, Alaska 
Canberra, Australia 
Glenoree, Ireland 


1928-1929 
1932-1933 

1934 

1937 


1.30 
1.45 
1.29 
1.28 


1.39 
1.75 
1.40 
1.40 



agreement, especially in view of the very large differ- 
ence in meteorological conditions at the various stations 
and the possibility that such conditions might affect 
the mobility of the atmospheric ion. 

Since the mobility of an ion is affected by impurities 
in the gas, it seems likely that atmospheric ions may be 
affected by impurities in the air. A sudden change in 
mobility, believed to be due to such causes, was found 
by Parkinson [35] at Huancaj^o, Peru (altitude 3300 m, 
mean pressure 518 mm). From carefully controlled 
mobility determinations and from simultaneous meas- 
urements of air conductivity and ion concentrations 
which were corrected for the lower-mobility ions caught 
by the ion counter, it was found that a sudden drop in 
mobility took place each morning at about seven o'clock 
local time. This drop occurred at the precise time when 
there was a large influx of molecular impm-ities into the 
atmosphere. The average values of k-\- and k— for the 
7-hr period before the influx of impurities were 2.40 
and 3.46, respectively. The mean values for the 7-hr 
period immediately following the influx were 2.00 and 
2.35, respectively. The change in negative-ion mobility 
was nearly twice as great as the change in positive-ion 
mobility. Thus it appears that the molecular impurities 
at Huancayo associate more readily with the negative 
than with the positive ion. 

Impurities in the atmosphere tend to be graded as to 
size, so that ions of a mobility lower than that of the 
small ion ai-e often, although not always, found within 
rather narrow mobility ranges. Pollock [37] in Sydney, 
Australia, observed a group (intermediate ion) with a 
mobility between 0.1 and 0.02 cm. A similar mobility 
group has been found in other locahties [14, 16, 47]. 
In some localities, on the other hand, there appears to 
be no such group [52, 56]. A lower-mobility group 
(around 10"' cm) first detected by Langevin [21] has 
since been observed in a number of localities, and the 
ions in this group are now called the "Langevin," or 



large, ions of the atmosphere. Ions of still lower mobility 
have been observed in some localities [17]. 

Pollock found that the mobility of the intermediate 
ion was a function of the vapor pressure of the atmos- 
phere, diminishing from around 0.1 to about 0.02 cm 
when the vapor pressure increased to about 17 mm, 
whereupon the ion was suddenly transformed into the 
large ion. Both Hogg [14] and Wait [47] examined this 
matter and neither found any tendency for the inter- 
mediate ion to be transformed into the large ion at any 
vapor pressure. Wait, however, found that the mobility 
of the intermediate ion was a function of the vapor 
pressure. At a pressure corresponding to mm the 
mobilitj^ was about 0.5 cm while at 30 mm pressure it 
was only 0.05 cm. 

Yunker [56] found a continuous mobility distribution 
in California. He presented a distribution in which the 
number of ions per mobility interval increases with 
increasing mobility. His results on artificially ionized 
air indicate that the concentration of ions of mobility 
down to 7 X 10"'' cm varies inversely with the nuclei 
concentration, which shows that the ions formed by 
charging of condensation nuclei have a still lower mo- 
bility. 

Nature of Slow Ions 

It is usually considered that a large ion is a charged 
condensation nucleus of the type discovered by Aitken 
[1]. This ion is usually singly charged, but multiply 
charged ions can exist [5, 15]. In general, nuclei appear 
to consist of some hygroscopic core around which a 
stable agglomeration of water molecules can form. 
Landsberg [20] has presented a detailed discussion of 
what is known of their properties. Sulphuric acid (a 
common product of combustion) and oxides of nitrogen 
probably play important parts in the formation of 
nuclei. Wright [55] discusses the matter of salt spray 
forming the core material for a nucleus which appears to 
be somewhat larger and is important in the atmosphere 
over the oceans and at some coastal places, but less 
important in mo.st inland localities. 

Pollock [37], in his announcement of the e.xistence of 
intermediate ions, considered them to consist of a 
"rigid nucleus enveloped by a dense atmosphere of 
water vapoiu-." Since the intermediate ion appears to 
exist only in certain localities, its nature probably 
varies greatly. If, as found by Wait [47], its mobility 
varies with water-vapor pressure in accordance with 
Blanc's law, then the size of the ion is probably con- 
stant. This argues against a hygroscopic ion. Hogg [16], 
working in London, detected intermediate ions the sizes 
of which were multiples of an aggregate of some 2000 
molecules. He assumed them to be composed of sul- 
phuric acid. 

Rate of Ionization 

The term ionization as used here refers to the produc- 
tion of ions, and not to ion concentration (as is some- 
times the case) . Small ions may be produced in air by a 
variety of methods, such as by chemical and mechanical 
means, by ultraviolet light of sufficiently short wave 



122 



ATMOSPHERIC ELECTRICITY 



length, by breaking drops, and by drifting snow and 
dust. Under particular circumstances one or more of the 
above-mentioned processes may add appreciably to the 
ion population of the air. None of these, however, are 
normally important as ionizers of the atmosphere. The 
chief ionizer in the lower stratosphere and the tropo- 
sphere, except in the lower atmosphere over land, is the 
cosmic rays. In the lowest kilometer or so over land, 
ionization of the air is due chiefly to radiations from 
radioactive matter in the earth and in the air. 

The average rate of ionization of the atmosphere q, 
over land and near the earth's surface, has been esti- 
mated by Hess [10, pp. 167-171] at about 10 pairs per 
cc per sec. This value is based on the average amount of 
radioactive matter in the earth and in the air and is 
summarized in Table II. According to this estimate, 
approximately half of the total ionization is due to 
radioactive matter in the air, one third is due to radio- 
active matter in the soil, and one sixth due to cosmic 
rays. The ionization due to cosmic rays and radioactive 
matter in the soil is probably more or less constant with 
time at a given station. That due to radioactive matter 
in the air, however, is subject to variations, since the 

Table II. Ionization ok the Air Near the Earth's 
Surface Over Land in Per Cent of Total 





Ionizing ray 


Total 


Ionizer 


a 


/3 


7 


Cosmic 
rays 


Radium \- „• 
Thoriumr ^'' 
Radium \- •, 
Thorium)'" ^°'^ 
Cosmic ra3^s 


30 
18 


1 
1 

1 


1 

32 


16 


33 
16 


Total 


48 


3 


33 


16 


100 







quantity of radioactive matter in the air varies with 
time. The amount of radioactive matter in the air 
depends upon two factors: (1) the rate at which it is 
dissipated in the atmosphere, and (2) the rate of exhala- 
tion from the soil. 

The rate of exhalation of radioactive gas from the soil 
is subject to considerable variation, being affected by 
such factors as temperature of the soil, wind force, 
dryness of soil, and covering on the ground [4, 57, 58]. 
The rate of dissipation in the atmosphere depends upon 
several factors, but particularly upon air turbulence. 
Zeilinger found a diurnal variation in the rate of exhala- 
tion from the soil, a maximum occurring in the morning 
hours and a minimum in the evening. A diurnal varia- 
tion curve with similar characteristics has also been 
found for the radon content of the atmosphere [57]. 

A systematic diurnal variation in the rate of ioniza- 
tion of air near the earth over land would be expected, 
with a maximum occurring in the morning and a mini- 
mum in the evening. Continuous observations on the 
rate of ionization have been reported at three stations, 
Canberra, Australia [13], Washington, D. C. [48], and 
Huancayo, Peru [35], in which diurnal variation curves 
were obtained. A curve for each of the three stations is 



shown in Fig. 1. The curves are of the type expected 
when each is plotted on local time. Slightly different 
methods were employed in measuring the ionization. 




5 8 10 12 14 16 

HOURS (LOCAL MEAN TIME) 



20 22 24 



Pig. 1. — Daily variation in ionization of the lower atmosphere. 

Hogg [13] measured the ionization of the air after it was 
drawn into a thick-walled sealed chamber. Wait [48] 
and Parkinson [35] measured the ionization in a thin- 
walled ionization chamber (the stopping power of the 
wall for alpha particles was equivalent to 1.5 cm of 
air). The values plotted for Huancayo represent the 
rate of ionization inside the chamber and must be 
multiplied by about 1.6 to correspond to the ionization 
of the atmosphere. 

Small-Ion Balance 

The processes of ion formation just described are 
balanced by the processes of small-ion destruction. One 
such process is the recombination between small ions of 
opposite signs. Ions of other mobility groups will also 
be active in neutralizing small ions. This is particularly 
true of the large ions. A third process is one not of 
neutralization but of the conversion of a small ion into 
a large ion by coalition of a small ion and a neutral 
condensation nucleus. The equation of ion balance for 
positive small ions, taking into account the processes 
mentioned so far, is 



q = aniUi + miNini -\- rnoNoni. 



(1) 



There is an analogous equation for the negative small 
ions. The symbols have the following meanings: q is the 
rate of small-ion formation (expressed in ion-pairs per 
cc per sec) ; a is the recombination coefficient for small 
ions; ni and nj are the concentrations of positive and 
negative small ions, respectively (in ions per cc); iV2 
is the concentration of negative large ions; and A''o is 
the concentration of neutral condensation nuclei. The 
constants rjn and ifw are known as combination coef- 
ficients. 

In general the small-ion concentration is accounted 
for by such an equation. In some places it is necessary 
to take into account the effect of intermediate ions, 
but their effect is always small compared to that of the 
large ions and uncharged condensation nuclei. Over 
land, the term due to recombination is generally small 
compared to the other terms, and equation (1) can be 
written: 



q = niivuNi + vioNo). 



(2) 

I 



IONS IN THE ATMOSPHERE 



123 



Now the balance of large ions, shown latei-, requires 
that 

i7ioA''oni = vuNini, (3) 



and similarlj' for the negative ions: 



(4) 



If one further assumes that (3) is equal to (4), then 
(2) can be rewritten as 



q = 2rii2niN2, 



(5) 



so that, if changes in q are neglected, the value of rii 
is approximately inversely proportional to A'^2. 

Processes which cause the destruction of small ions 
other than those involving combination wth small or 
large ions or condensation nuclei can play an important 
part under some conditions. Large particles such as 
smoke and dust can remove small ions [2, 48]. In the 
atmosphere over the oceans the most important process 
of destruction of small ions is recombination, but 
here the influence of nuclei is perceptible in the balance 
of small ions [44]. In this connection it is intei'esting to 
mention the results of a, long series of observations of 
atmospheric conductivity over the oceans. A steady 
decrease has been noted since 1912, indicating that even 
here there is a gradual accumulation of atmospheric 
pollution, due apparently to the increasing industrializa- 
tion over the world [48]. 

Recombination of Small Ions 

This subject has been extensively studied, both theo- 
retically and experimentally. The reader is referred to 
the exhaustive treatment given by Loeb [22], and by 
Jaffe [18]. The subject cannot be pursued here ; however, 
a word about columnar recombination is in order. In the 
high ion-density track or column left by an alpha parti- 
cle there will be a high rate of columnar I'ecombination. 
Thus the effective rate of ion formation is less than 
that which actually occurs. Only those ions which escape 
from the column have a life of any appreciable length. 
The number escaping will be increased by winds and 
eddy diffusion. In atmospheric electricity this matter 
has received but little consideration. It has been dis- 
cussed by Nolan [31]. 

The value of the effective recombination of small 
ions is usually taken as 1.6 X 10""^ cc per sec for air at 
atmospheric pressure [6, p. 178]. However, Luhr and 
Bradbury [23] give a value of 1.23 X 10" «, Sayers 
[38] gives 2.4 X 10~^ and Nolan [31] gives a value of 
1.4 X 10- «. 

Combination of Small Ions with Condensation Nuclei 

The theory of small-ion combination with condensa- 
tion nuclei or large ions has received less attention than 
has the theory of recombination. If all variables in the 
equations of small-ion balance were measured, it would 
be possible to determine the value of combination 
coefficients. Usually this is not done, but relations be- 
tween parameters are assumed. If it is asumed that 
equation (3) is equal to equation (4), it follows that: 



No/Nl = J?2l/'?20, 
N0/N2 = 7712A10, 

N1/N2 = vnTii/viirii. 



If we assume that Ni = N2 = 
tionships : 



A'', we obtain the rela- 



No/N = )?2iA2o = ';i2Aio, 

ni/n2 = I?2o/'7lO = V2l/Vl2, 

which were assumed by Nolan and de Sachy [26]. 
Whipple [53] has deduced the following equations, which 
are sometimes used as an auxiliary relation between 
parameters : 



1712 = i/io + 47refci, 
7721 = '720 + 4xefc2, 



(6) 



where ki and k2 represent the mobility of the positive 
and negative small ion, respectively. 

Almost every observer has used a different method 
of determining these combination coefficients. Gish and 
Sherman [9] gave a thorough discussion of these meth- 
ods together with a table of values prior to 1940. More 
recent values have been summarized by Parkinson 
[36], and Table III shows representative values. 

Table III. CoMBI^fAT^o^r Coefficients (in units of 10"*) 





"10 


"m 


'l! 


'21 


Least value . ... 


0.4 
6.8 
0.6 


0.6 
7.6 
1.1 


2.2 

8.7 
2.4 


2.5 


Greatest value 


9.7 




4.5 







It is not surprising that these values vary so widely 
when it is remembered that various methods of deter- 
mination have been used. Also it is not reasonable to 
expect that the combination coefficients would be pre- 
cise universal constants since they depend upon the 
nature {i.e., the mobility) of slow ions, which will vary 
with conditions and hence from place to place. Also, 
no notice is usually taken of the distribution of mobil- 
ities involved in the ions responsible for the destruction 
of small ions, nor is an allowance made for intermediate 
ions as distinct from large ions. 

Several investigators [32, 33] have found that the age 
of the large ion has an influence on the value of the 
combination coefficient, the coefficient becoming higher 
the older the nuclei. This is probably due to an increase 
in the size of the nuclei with age, owing to coagulation. 

Large-Ion Balance 

If we assume that a distinct group of large ions exists, 
then we can speak of their balance just as we do in the 
case of small ions. One method of formation of large 
ions is the process which has been mentioned above as 
one which destroys small ions, namely the fusion of a 
small ion with a neutral condensation-nucleus. The 
other process of destruction is the neutralization of 
charge by a small ion of opposite sign. There will also 
be a recombination term, similar to that for small ions, 
and a linear term ^N to account for diffusion [30]. We 
can write Q for the formation of large ions by other 



124 



ATMOSPHERIC ELECTRICITY 



methods; then the equation of positive large-ion balance 
becomes 

dNi/dt = Q + VioniNo — r]->in2Ni 

- yN^N, - fiVi. (7) 

There will be a similar equation for the negative large 
ions. In this case the value of Q will not necessarily be 
equal for the positive and negative large ions, for the 
situation is not as simple as for small ions where the 
formation is principally due to a process wherein an ion 
pair is produced. 

Kennedy [19] and Nolan [30] found values of 7 of 
the order of 10"'*. Hogg [12] reported a value about ten 
times this, but failed to take into account coalition of 
neutral nuclei and diffusion or falling out of larger 
nuclei as a means of dimunition of nuclei. Wait and 
Torreson [51] found that the value of 7 varies with the 
age of the ion. In a later study, Wait [48] found that for 
singly charged ions the value of 7 could be expressed as 
a function of the mobility k of the ion. A provisional 
value of this relationship is given by the equation 

7 = 1.25 X 10-" kr*, 

which appears to hold for all mobilities between that of 
the large and that of the small ion. The measured value 
of 7 for /c = 3.2 X 10-^ was 3.1 X 10" ^ In the free 
atmosphei'e away from sources of large ions the terms 
Q, yNiN^, and ^Ni are usually so small they can be 
neglected, and (7) reduces to 

dNi/dt = vioniNo — vnUtNi, 

and for large-ion equilibrium conditions, 

VioniNo = Vnii^Ni, 

which is equation (3). Equation (4) represents the 
analogous equation in the case of the negative large 
ions. 

Ionic Concentrations in the Lower Atmosphere and 
Their Variations 

Both large- and small-ion concentrations vary con- 
siderably from place to place and from time to time at a 
given place. Over land, the two usually vary systemati- 
cally but in opposite directions, both during the day 
and throughout the year. 

The large-ion content (in ions per cc) of the air over 
the oceans averages onlj^ a few hundred of each sign. 
More extensive measurements have been made of the 
condensation-nuclei content of the air over the oceans 
from which estimates may be made of the large-ion 
content. Landsberg [20], making use of all available 
measurements at the time, estimated that the average 
nuclei content of the air over the oceans was 940. Hess 
[11] more recently found an average over the Atlantic, 
between America and Europe, of 527 on one leg of a 
cruise and 659 on another leg. On Cruise VII of the 
Carnegie [44], the average nuclei concentration was 
1370 over the Atlantic and 2350 over the Pacific. From 
all of these results one would estimate between 100 and 
200 large ions of each sign for the air over the Atlantic 
and two to three times this number over the Pacific. 



The large-ion content over the oceans, as estimated on 
the basis of the number of small ions found during 
Cruise VII, is around 180 of each sign [44], which is in 
reasonably good agreement with the estimates above. 
No diurnal variation was found in the condensation- 
nuclei content of the air over the oceans during Cruise 
VII, from which one might surmise that the large-ion 
content would likewise be constant through the day. 

Over land, Landsberg [20] estimated that the average 
condensation-nuclei content of the air in country dis- 
tricts was around 10,000 per cc, in towns around 30,000, 
and in cities around 150,000. The corresponding large- 
ion content might accordingly be estimated at between 
1000 and 2000 for a country area, between 5000 and 
6000 for a town, and between 20,000 and 30,000 for a 
city. These must be regarded as rough estimates only. 

Most observations on the condensation and large-ion 
content of the air over land have been taken in the 
vicinity of human habitations. Both the annual and 
diurnal variations as well as the absolute values are 
greatly affected by human activities. When observed 
sufficiently far from industrial activities of man, the 
large-ion content, like the condensation-nuclei content 
of the air, shows a maximum during the winter when 
heating of homes is greatest, and a minimum in the 
summer. For a similar reason, the condensation-nuclei 
content of the air generally shows a maximum during' 
the middle of the day [15, 20, 26, 46, 56]. The diurnal 
variation in large-ion concentration obtained by Yunker 
[56], on the other hand, was more or less opposite to 
this. The curve for large ions found at Washington [49] 
is likewise quite opposite and similar to Yunlcer's curve, 
both being plotted on local time. Torreson [43] first 
pointed out the discrepancy between the condensation- 
nuclei curves and the large-ion curves at Washington, 
and Wright [54] suggested an explanation based upon 
a variation in size of the condensation nuclei with 
relative humidity. Sherman [40] could find no evidence 
of a diurnal variation in the ratio of uncharged to 
charged nuclei in the aii', as required by Wright's 
hypothesis. This apparent paradox has not yet been 
explained, but it raises the question whether condensa- 
tion-nuclei counts tend to include relatively large parti- 
cles while the large-ion counts include smaller particles. 
Additional experiments will be required to find an 
answer to the question as to why the two curves are of 
such different character and to ascertain if a similar 
difference is to be found at other places. 

Over the oceans, even though the rate of small-ion 
production is less than that over land (only 10 to 15 
per cent as great), the small-ion concentration in the 
two areas usually differs but little. This is accounted 
for by a smaller number of large ions over the pceans 
and consequently a slower destruction rate of the small 
ions. Over the oceans, the average small-ion content of 
the air was about 500 and 400, respectively, for the 
positive and negative ions during Cruise VII of the 
Carnegie [44]. Over land the concentration of each sign 
varies from around 100 over polluted areas to about 
1000 for areas unpolluted with industrial smokes and 
gases. 



IONS IN THE ATMOSPHERE 



125 



The small-ion content of the lower atmo.sphei'e is 
generally lowest during the winter months and highest 
during the summer, just opposite to that found foi' the 
large-ion content. The values usually reach a maximum 
during the morning hoiu's and a minimum during the 
afternoon. This type of variation, while largely con- 
trolled by the variation in large-ion content of the air, 
also depends to some extent upon the variations in the 
I'ate at which ions are produced, which, according to the 
curves of Fig. 1, is greatest during the early morning 
hours. 

Variation in Ion Concentration of the Atmosphere with 
Height above Ground 

The value of the large-ion concentration of the atmos- 
phere at various heights above the ground can only be 
inferred from the ^'alues of condensation nuclei obtained 
at various altitudes. Wigand [20] made fourteen balloon 
flights on which condensation nuclei were measured. 
A rapid decrease in concentration with altitude was 
found; at a height of 3 km the concentration was only 
3 per cent of that at ground level. 



Much more information is available concerning the 
value of the ratio n\ln%, how it varies and why, than 
there is concerning the ratio N1/N2. Moussiegt [25], 
from observations in the Alps, found mean values of 
2214 and 2335, respectively, for A'': and N2, from which 
one would deduce a value of 0.95 as the ratio of N1/N2. 
Hogg [15], in Canberra, Australia, found a mean value 
for this ratio of 1.22. In Washington, D. C, continuous 
I'ecords (unpublished results) of large, small, and inter- 
mediate ion concentration of air, alternating each week 
between the positive and negative ions, were made 
during September and December, 1935. Since these 
data are not strictly simultaneous, the ratios can be 
regarded as only approximate. In view of the paucity of 
published data from which a comparison of positive- 
and negative-ion content can be made, a summary of 
these data seems worth while and is given in Table 
IV. The large-ion concentrations in ions per 10~^ cc are 
represented by A^i and A^2, while Mi, M2, and rii, 712 
represent the positive and negative intermediate-ion 
and the positive and negative small-ion concentrations, 
respectively, in ions per cc. The ratios M1/M2 and ni/n2 



Table IV. Means of Various Hourly Values of Various Elements in Washington 



Means of 


Elements 


Month (1935) 




iVi 


Ni 


M, 


M2 


m 


M2 


JVi/iVi 


M,/M2 


Kl/»2 




5 largest. 


77.2 
35.8 
51.1 


72.4 
27.3 
42.8 


121 

94 

107 


126 

91 
108 


284 
ISO 
229 


266 
145 
212 


1.49 
1.00 
1.10 


1.05 
0.95 
1.00 


1.19 
1.01 
1.10 




5 smallest 


September 


All values 






5 largest 


79.3 
46.8 
60.8 


74.0 
38.5 
48. 8 


167 
139 
153 


195 
139 
170 


169 
128 
188 


159 
108 
173 


1.27 
0.98 
1.12 


1.01 
0.90 
0.96 


1.22 
1.01 
1.12 




5 smallest 




All values 









The values of the small-ion concentration made on 
thirteen balloon flights by various observers and that 
deduced from Explorer II air-conductivity measure- 
ments have been summarized by Gish [6, p. 194]. He 
concludes that the concentration increases roughly by 
1000 ions per cc (one sign) for each 2-km increase in 
altitude. This rate of increase is true up to an altitude 
of about 6 km, after which it gradually diminishes, 
according to the Explorer II data, to less than half 
this value at 14-km altitude. 

Ratio of Positive-Ion to Negative-Ion Concentration 

A relationship between the ratios N1/N2 and ?ii/n2 has 
been deduced by Gish [6, p. 183] from the equilibrium 
equations and is given by the equation 

(rii/niT- = bN,/aN2, 

where a = 77io/j?2i and b = r?2o/'7i2. If one assumes that 
^10/1720 = '712/1721, then from the equation above it 
follows that 

(niM)^ = iv2o/vioyNi/N2, 

which is the relationship assumed by Nolan and de 
1- achy [26] 



show no consistent diurnal variation, while the ratio 
N1/N2 "\'aries more or less in a manner opposite to that 
of the large-ion content [49]. 

During fair weather the average concentration of 
positive small ions exceeds that of the negative small 
ions by 10 or 20 per cent. Particularly at certain sta- 
tions, the ratio ni/n2 varies in a manner similar to the 
variation of the earth's field (electrode effect). This is 
due to the repulsion of negative ions by the negatively 
charged ground. During a thunderstorm, because of the 
intense electric field with frequent changes in sign, the 
ratio undergoes frequent changes in value, say from a 
very high to a very low value and vice A'ersa, usually 
several times during a storm. 

Mean Life of an Ion 

The mean life of an ion is the time interval between 
formation and destruction of the average ion. For small 
ions the mean life r„ in seconds, for the case when large- 
ion concentration is sufficiently small, is given by the 
equation 

T„ = n/q, (8) 

in which n represents the small-ion concentration and 
f/, the rate of ionization (rate of small-ion formation). 



126 



ATMOSPHERIC ELECTRICITY 



When the large ions are numerous, then in accordance 
with the assumptions made in deriving (5), 



1 



Tn 



2r]liNi 



(9) 



Over the oceans the value of t„ will generally be around 
5 or 6 min. Over land, in areas where the large ions are 
few, the mean life r„ may be expected to be only 10 or 
20 per cent of the above. In localities where large ions 
are numerous, the value of t„ will be still smaller, prob- 
ably only 5 per cent or so of the ocean value. 

The mean life tn of the large ion is given approxi- 
mately by the equation: 

Over the oceans and over land where the large ions are 
not very numerous, the value of t^ may be between 15 
and 20 min. In areas where the large ions are numerous, 
the value of t^ may easily exceed an hour. 

Because of the relatively short life of the small ion, 
the small-ion concentration may be expected to follow 
with little lag those factors which tend to produce a 
change in the concentration. Much greater lag may be 
expected in the changes of large-ion concentrations. 

Outstanding Problems in the Field of Atmospheric Ions 

A number of investigations have been carried out for 
the purpose of evaluating the factors which control or 
regulate the small-ion content of the lower atmosphere. 
There is growing evidence that some of the factors, for 
example the value of the combination coefficients be- 
tween the small ions and the charged and uncharged 
condensation nuclei, may vary from place to place. This 
is probably due to a difference in character of the nuclei 
which results in a difference in nuclei size. A close 
correlation would therefore probably be found between 
the values of the combination coefficients and the mobil- 
ity of the large ion. In future work, a recognition of this 
possibility may assist in harmonizing results which 
otherwise might appear to be inconsistent. 

Another small-ion regulating factor which is difficult 
to evaluate is q, the rate of ionization of the atmosphere. 
Probably the most promising method of evaluating this 
factor is through the use of a thin-walled ionization 
chamber. This cannot be accomplished, however, with- 
out certain difficulties. Cognizance must be taken of 
the low radioactive content of the air within the cham- 
ber compared to that of the outside air and of the fact 
that the ionization within the chamber will depend 
upon the wall thickness and upon the particular voltage 
applied to the central electrode. The latter arises from 
the fact that complete saturation is never achieved, due 
probably to columnar ionization inside the chamber. 
A full discussion of this problem is not possible within 
the limits of this article. 

It is quite probable that meteorological conditions 
play an important role in altering the efficiency of some 
or all of the small-ion regulating factors. Temperature, 
humidity, and pressure of the atmosphere, for example, 
are likely to exert an influence on such factors as com- 



bination coefficients, recombination coefficients, and the 
mobility of ions. There is urgent need for careful experi- 
ments designed to secure much-needed information 
along such lines. 

Multiply charged large ions should be examined as to 
regularity of, and conditions of, occurrence and as to 
their effect on large-ion mobility and on establishment 
of small-ion equilibrium conditions. 

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2. BoYLAN, R. K., "Atmospheric Dust and Condensation 

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4. CuLLEN, T. L., "On the Exhalation of Radon from the 

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10. Hess, V. F., The Electrical Conductivity of the Atmosphere 

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12. Hogg, A. R., "Some Observations on the Average Life of 

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17. Israel, H., and Schulz, L., "The Mobility-Spectrum of 

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19. Kennedy, H., "The Large Ions in the Atmosphere." 

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IONS IN THE ATMOSPHERE 



127 



20. Landsberg, H., "Atmospheric Condensation Nuclei." 

Beilr. Geophys., Supp., 3: 155-252 (1938). 

21. Langevin, p. "Sur les ions de I'atmosphere." C. R. Acad. 

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22. LoEB, L. B., Fundamental Processes of Electrical Discharges 

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23. LuHR, O., and Bradbury, N. E., "Corrected Values for the 

Coefficient of Recombination of Gaseous Ions." Phys. 
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24. Mauchly, S. J., "Studies in Atmospheric Electricity Based 

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Res. Dept. Terr. Magn., Carneg. Instn. Wash. Publ. 
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25. MoussiEGT, J., "Mesures de la conductibilite et de I'ionis- 

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26. Nolan, J. J., and de Sachy, G. P., "Atmospheric lonisa- 

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27. Nolan, J. J., and Nolan, P. J., "Further Observations on 

Atmospheric lonisation at Glencree." Proc. R. Irish 
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28. "A New Method for Counting Atmospheric Ions and 

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29. "Atmospheric Electrical Conductivity and the Cur- 
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30. Nolan, P. J., "Experiments on Condensation Nuclei." 

Proc. R. Irish Acad., (A) 47: 25-38 (1941). 

31. "The Recombination Law for Weak lonisation." 

Proc. R. Irish Acad., (A) 49: 67-90 (1943). 

32. and Galt, R. I., "The Equilibrium of Small Ions and 

Nuclei." Proc. R. Irish Acad., (A) 50: 51-68 (1944). 

33. Nolan, P. J., and Fahy, E. F., "Experiments on the Con- 

ductivity of Atmospheric Air." Proc. R. Irish Acad., 
(A) 50: 233-256 (1945). 

34. OvERHAUsER, A. W., "The Clustering of Ions and the 

Mobilities in Gaseous Mixtures." Phys. Rev., 76: 250- 
254 (1949). 

35. Parkinson, W. D., "Factors Controlling the Atmospheric 

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Terr. Magn. atmos. Elect., 53: 305-317 (1948). 

36. Review of the Literature on the Ion Balance of the Lower 

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37. Pollock, J. A., "A New Type of Ion in the Air." Phil. 

Mag., 29: 636-646 (1915). 

38. Sayers, J., "Ionic Recombination in Air." Proc. roy. Soc, 

(A) 169: 83-101 (1938). 

39. Sherman, K. L., "Atmospheric Electricity at College- 

Fairbanks Polar Year Station." Terr. Magn. atmos. Elect., 
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40. "Total and Uncharged Nuclei at Washington, D. C." 

Terr. Magn. atmos. Elect., 45: 191-204 (1940). 

41. Swann, W. F. G., "On Certain New Atmospheric-Electric 

Instruments and Methods." Terr. Magn. atmos. Elect., 
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42. Thomson, J. J., Conduction of Electricity Through Gases, 

3rd ed. Cambridge, University Press, 1933. (See p. 7) 

43. Torreson, O. W., "On the Value of the Ratio of the 

Number of Uncharged Nuclei (A^o) to the Number of 
Charged Nuclei of one Sign (7V±) at Washington, D. C." 
Terr. Magn. atmos. Elect., 39: 65-68 (1934). 

44. and others, "Scientific Results of Cruise VII of the 

Carnegie. Oceanography III, Ocean Atmospheric Elec- 
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45. Torreson, O. W., and Wait, G. R., "Measurements of 

Total Nuclei, of Uncharged Nuclei, and of Large Ions in 
the Free Atmosphere at Washington, D. C." Terr. Magn. 
atmos. Elect., 39: 47-64 (1934). 

46. Wait, G. R., "Diurnal Variation of Concentration of Con- 

densation-Nuclei and of Certain Atmospheric-Electric 
Elements at Washington, D. C." Terr. Magn. atmos. 
Elect., 36: 111-131 (1931). 

47. "The Intermediate Ion of the Atmosphere." Phys. 

Rev., 48: 383 (1935). 

48. "Some Experiments Relating to the Electrical Con- 
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Sci., 36: 321-343 (1946). 

49. and Torreson, O. W., "The Large-Ion and Small-Ion 

Content of the Atmosphere at Washington, D. C." 
Terr. Magn. atmos. Elect., 39: 111-119 (1934). 

50. "Diurnal Variation of Intermediate and Large Ions 

of the Atmosphere at Washington, D. C," Terr. Magn. 
atmos. Elect., 40: 425-431 (1935). 

51. "Recombination of Ions from Gas Flames." Phys. 

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52. Weiss, R., und Steinmaurer, R., "Messungen der Luf- 

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(1937). 

53. Whipple, F. J. W., "Relations Between the Combination 

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39: 277-280 (1934). 

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3-12 (1940). 

56. Ydnker, B. a., "The Mobility Spectrum of Atmospheric 

Ions." Terr. Magn. atmos. Elect., 45: 127-132 (1940). 

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Elect., 40:281-294 (1935). 

58. Zupancic, p. R., "Messungen der Exhalation von Radium- 

emanation aus dem Erdboden." Terr. Magn. atmos. 
Elect., 39: 33-46 (1934). 



PRECIPITATION ELECTRICITY 

By ROSS GUNN 
Physical Research Division, U. S. Weather Bureau 



Introduction 

Although atmospheric electricity does not play an 
important part in the control of world-wide weather 
phenomena, it does have considerable bearing on spe- 
cial weather problems. Because of the basic electrical 
nature of all matter, most mechanical and thermody- 
namical energy transformations are accompanied by 
some type of electrical phenomenon. It is not surprising, 
therefoi'e, that the production of precipitation in the 
atmosphere frequently gives rise to interesting and im- 
portant electrical effects. These phenomena share many 
of the peculiarities of weather because of the extreme 
complexity of charge production and transport proc- 
esses in the atmosphere. One serious difficulty in the 
proper evaluation of precipitation electric phenomena 
is that the data thus far collected have been limited to 
a relatively few geographical regions and with few 
exceptions have covered only short periods of time. 
Many of the data are contradictory. 

In view of the complexity of the electrical phenomena 
accompanying precipitation, it might appear that the 
most rapid progress on basic problems would be made 
if laboratory investigations were undertaken. However, 
it is apparent that this would be extraordinarily diffi- 
cult for the same reason that investigations of weather 
in the laboratory have met with considerable difficul- 
ties. Electrification of the atmosphere and of precipi- 
tation is related to the characteristics and development 
of cloud structures, and these have not yet been suc- 
cessfully reproduced under controlled conditions. The 
scientist is forced, therefore, to collect data wherever 
and whenever available and to attempt to deduce from 
them the main characteristics and important processes 
of nature. 

The principal practical problems of precipitation 
electricity that require intensive work are (1) to de- 
scribe the detailed electrical processes responsible for 
the production of lightning, (2) to describe the mech- 
anisms responsible for the maintenance of the observed 
negative free charge on the surface of the earth, and 

(3) to describe those processes that transfer free elec- 
trical charge to aircraft flying through natural precipi- 
tation and to devise a method for counteracting such 
processes. Solution of these practical problems requires 
a detailed understanding of other still more basic ques- 
tions: (1) How is a free electrical charge placed on 
precipitation? (2) Why does charge of a selected sign 
appear principally upon the larger precipitation ele- 
ments? (3) What are the mechanisms responsible for 
the separation of positive and negative charges? and 

(4) How large are the electric fields so produced? Quan- 
titative understanding of these fundamental problems 



will provide a suitable foundation for the solution of 
the more practical problems. 

Earth electrification processes that become manifest 
through easily obtainable measurements are intimately 
related to a dual basic process consisting first of the 
deposition of free charge on precipitation particles and 
then of the subsequent mechanical separation of charges 
having opposite signs. Mechanisms responsible for plac- 
ing a free electrical charge of selected sign on the pre- 
cipitation particles are not well understood, but they 
are basically related to atomic forces that are both 
physical and chemical in nature. 

The occurrence of electrification and of coexisting 
available electrical energy implies the expenditure of 
mechanical work to establish the electrified state. In 
the earth's atmosphere this systematic mechanical Avork 
comes principally from gravitational forces and acceler- 
ations due to turbulent atmospheric motion, acting on 
precipitation particles. Large-scale separation of elec- 
trical charges will occur only when the acting forces 
operate on particles of one sign in a way quite different 
from the way they operate on particles carrying the 
opposite electrical charge. Because precipitation par- 
ticles normally fall in the earth's atmosphere, the 
observed separation of charges always implies that the 
aerodynamic characteristics of carriers of the positive 
charge are notably different from the characteristics of 
carriers of the negative charge. This aerodynamic con- 
trast between the particles carrying opposite charges 
is of importance in the description of all large-scale 
atmospheric electrifications. 

Observed Free Electrical Charge on Precipitation 

Early investigators were of the opinion that the free 
electrical charge carried to the earth by rain was ade- 
quate to replenish the normal discharge current ob- 
served in fair-weather areas throughout the earth. 
Later work has recognized that other processes are also 
important, but the original ideas stimulated the first 
measurements. The literature on the subject is contra- 
dictory in many cases, and the actual values of free 
electrical charge carried down by precipitation particles 
differ so much from place to place and with different 
meteorological situations that average values are of 
questionable significance. Better agreement between 
various observers is secured if the electrical character- 
istics of precipitation are classified in accordance with 
three distinct types of rainfall: (1) continuous or quiet 
rain (Landregen), (2) shower or squall rain (Boenregen), 
and (3) electrical storm rain (Gemiter) . This useful classifi- 
cation was adopted by Gschwend in his measurements 



128 



PRECIPITATION ELECTRICITY 



129 



of charge and mass of individual falling raindrops re- 
ported in 1920 [11]. 

Continuous or Quid Rain. Quiet rain, usually asso- 
ciated with smaller droplets, carries relatively smaller 
charges per drop than storm rain and is more likely to 
be predominantly of one sign. The majority of experi- 
menters have found that quiet rain is usually positive, 
although examples of continuous negative rain are 
known. The ratio of positive to negative charges re- 
ported generally varied from 1.1 to 1.5 when adequate 
samples were taken. In spite of the excess observed 
positive charge, it Avas found that the negative charge 
per droplet in most cases was greater than the positive 
charge per droplet. This implies, and measurements 
show, that usually a larger number of positively 
charged droplets fall. A dependence upon the rate of 
rainfall has usualty been observed. A long series of 
measurements by Chalmers and Pasquill [4] in Eng- 
land showed that the number of particles carrying posi- 
tive charges was some 70 per cent more than the num- 
ber carrying negative charges, and that the total 
positive free charge delivered at the earth was some 30 
per cent greater than the negative. It is interesting to 
note in this connection that, if data are collected over 
a sufficiently long period, the net free transported 
charge may be a small fraction of the total. For exam- 
ple, Scrase [23] measured the convected charge con- 
tinuously for a two-year period. His results showed that 
positive charges predominated one year and negative 
the other, but for the entire interval the positive charge 
exceeded the negative by 10 per cent. 

Shower or Squall Rain. Squall-type showers share 
the electrical characteristics both of quiet rain and of 
rain falling in typical electrical storms. Wide excursions 
in the electrical characteristics are normally observed. 
The analysis of rain falling from postthunderstorm 
showers and from those that have not quite proceeded 
to the point of active charge separation will be of the 
utmost value in determining the basic precipitation 
charging processes. 

Electrical Storm Rain. The rain falling in a typical 
electrical storm is usually characterized by large droplets 
and large free charges that approximate a few hun- 
dredths of an electrostatic unit per drop. Gsch«'end 
[11] pointed out the remarkable fact that such rain 
frequentljr changes its sign. It has been found in active 
storms that after a very few consecutive droplets of 
one sign had been measured the chance of capturing a 
droplet having an opposite sign was very large. The free 
charge brought down by individual droplets falling 
from active thunderclouds has been measured on the 
ground by Gschwend [11], Banerji and Lele [3], and 
Gunn [12]. Gschwend found that the largest charges 
were associated with positi\'e droplets, while the other 
experimenters found the largest charges associated with 
negative ones. In very active electrical storms, Gunn 
fovmd a general trend connecting the chai'ge on a drop- 
let and its radius. The electrification of these droplet,-' 
increased on the average until an electric field that 
approximated 2.5 esu cm~' was established on the sur- 
face of the droplets. Negatively charged droplets were 



nearly twice as massive as the positively charged ones, 
and each carried about 25 per cent more charge. 

The sign and magnitude of the integrated free charge 
transported to the earth by precipitation in electrical 
storms is uncertain. A number of measurements in 
thunderstorms have shown that negative charge is usu- 
ally transferred to the earth by the acting mechanisms. 
For example, Banerji [1] has estimated that the excess 
negative charge convected to the ground by rain falling 
from an active thundei'storm in India was 2 X 10^ 
coulombs. 

The electrical state in an active storm is so compli- 
cated and confused that there is doubt as to the value 
of precipitation data as a guide to the interpretation of 
basic electrical processes. This uncertainty in interpre- 
tation has become serious as a result of a recent paper 
by Simpson [25]. He has presented evidence suggesting 
that the charge on falling rain is deposited by conduc- 
tion or corona currents discharged near the surface of 
the earth by the electric fields usually present. Al- 
though a number of earlier experimenters looked in 
vain for such a correlation, Simpson now reports a good 
correlation between the sign of the free charge and the 
direction of the electric field. A careful check of the 
facts in this matter by independent observers is badly 
needed.^ 

Measurements taken in an aircraft at various alti- 
tudes up to 26,000 ft have been reported by Gunn [14]. 
These measurements were made in regions far above 
surface corona discharges and maj' be the only ones 
that give a clear-cut indication of the charge-producing 
mechanisms in the earth's atmosphere. In a weak cold 
front exhibiting no thunderstorm activity, positive 
charges averaging 0.033 esu per drop were observed 
from 10,000 to 26,000 ft. Negative charges averaging 
0.040 esu per drop were measured between 4000 and 
20,000 ft. Positive particles were not observed below 
10,000 ft and negative ones were not detected above 
20,000 ft. The freezing level during these measure- 
ments was at 11,000 ft. Direct measurement in the 
vicinity of the plane showed that the electric field did 
not exceed 25 v cm~', and therefore thunderstorm ac- 
tivity was negligible. A coherent set of similar data [15] 
taken in an active thunderstorm gave notably greater 
free charges on the precipitation and suggests that the 
interpretation of such collected data will be extraordi- 
narily difficult. 

Snow. Gschwend made a nimihcr of measurements 
of the charge carried by individual snowflakes. Positive 
charges, in general, exceeded negative charges, and it is 
important to note that the charge on newly formed 
snow is nearly one hundred times larger than the charge 
on quietly falling, and presimiahly aged, snowflakes. 

Nakaya and Terada [20] found that snow carried a 
preponderately negative charge unless the flakes had 
frozen water droplets attached. Recently, Pearce and 
Currie [22] remarked on the large number of essen- 

1. (Note addoil in proof.) W. C. A. Hutchinson and J. A. 
Chalmers have just published a paper, "The Electrical Charges 
and Masses of Single Raindrops," Qiiarl. ./. R. meteor. Soc, 
77;S5-95 (1951), that provides needed data on this subject. 



130 



ATMOSPHERIC ELECTRICITY 



tially neutral snowflakes. However, of the flakes meas- 
ured, they found free positive charges on twice as many 
flakes as carried negative charges. They also found that 
snow drifting over the ground was strongly negative. 
Chalmers and Pasquill [4] reported that snow is pre- 
dominantly negative. It seems apparent from the lit- 
erature and from other measurements that the sign 
and magnitude of the charge on falling snow depends 
critically upon its crystalline structure and mode of 
formation. As an illustration of this fact, this author 
found that snowflakes falling quietly with an average 
velocity of 48 cm sec~' carried average positive charges 
of 0.00067 esu, whereas simultaneously falling negative 
flakes of average charge 0.0010 esu fell with a velocity 
of 80 cm sec~^ The difference in sign was definitely 
correlated with the rate of fall. It is probable that the 
rate of fall is determined by the structure and density 
of the flake, which, in turn, is determined by its mode 
of formation. It is a fair inference from the data, there- 
fore, that the opposite electrical charges result from 
grossly different developmental histories. 

Average values of free charge carried by both posi- 
tive and negative individual droplets of various kinds 
of precipitation, as measured by Gschwend [11], 
Banerji and Lele [3], Chalmers and Pasquill [4], and 
Gunn [12, 14, 15] are summarized in Table I. 

Table I. Average Free Electeical Charge on 
Individual Droplets (esu X 10^) 















— — 












Electri- 


ea 


nj 


Observer 


Altitude 

(ft) 




Quiet 
rain 


Shower 
rain 


cal 
storm 




ll 






O 






rain 


a 


en 


Gschwend 


surface 


-1- 


0.24 


1.75 


8.11 


0.09 


5.64 


(1921) 




— 


0.53 


5.43 


5.88 


0.06 


4.78 


Banerji and 


surface 


+ 




6.4 


6.9 






Lele (1932) 




— 




6.7 


7.3 






Chalmers and 


surface 


+ 


2.2 


1.3 


3.7* 




10.5 


Pasquill 




— 


3.0 


2.3 


9.2* 




5.7 


(1938) 
















Gunn (1947) 


4,000 
12,000 
20,000 


+ 
+ 

+ 




24 

41 

100 

63 








Gunn (1949) 


surface 


+ 






15 
19 


0.67 
1.0 




Gunn (1950) 


5,000 
10,000 
15,000 
20,000 


+ 
+ 
+ 
+ 






81 

63 

148 

112 

123 

76 

52 

62 







* Actual lightning activity doubtful. 



Cloud Elements. If raindrops are formed by the as- 
sociation of cloud elements, it is obvious that the free 
electrical charge collected on cloud particles is of fun- 
damental importance. A number of measurements have 
been made on the charges carried by clouds and fog, 
notably by Wigand [27]. He found that in a dry fog the 



cloud elements carried a positive electrical charge, but 
sometimes negative charges were measured. The mag- 
nitude of the charge varied from a few to a few hun- 
dred elementary charges. Using a specially instru- 
mented aircraft [18], the author made a number of 
measurements of the charges on cloud particles in small 
swelling cumulus clouds and found that the charges 
were usually negative. The average charge on each 
element was estimated to approximate 22 elementary 
charges. Scrase [24] found that cloud elements in heavy 
wet fogs frequently carried a negative charge approxi- 
mating 35 elementary units. Accumulation of informa- 
tion on the electrical charges carried by cloud droplets 
under various meteorological conditions is urgently 
needed. 

Processes Responsible for the Electrification of Pre- 
cipitation 

Because all large-scale atmospheric electrifications 
derive their energy originally from expenditure of me- 
chanical or gravitational work and because this work 
can be converted only when a free electrical charge is 
attached to some physical entity like a raindrop, it is 
of utmost importance to understand in detail the physi- 
cal processes whereby free charge, of either sign, can 
be systematically deposited on droplets. One of the 
outstanding characteristics of precipitation elements in 
the atmosphere is the enormous surface area exposed 
to the atmospheric ions and to the chemical activity of 
the air. It has been noted frequently that precipitation 
elements in the air share many of the remarkable prop- 
erties of a colloidal suspension. 

Droplet charging processes may be divided into two 
major categories: first, charging processes which are of 
a basic nature and dependent upon the physical and 
chemical properties of water and air; and second, charg- 
ing processes which are critically dependent upon spe- 
cial environmental conditions. 

Basic Processes. As a common example of electrifi- 
cation by a basic process, one may mention the separa- 
tion of electricity produced by friction. The rubbing 
together of materials having contrasting physical prop- 
erties usually results in the selective transfer of elec- 
trons in the outer orbits from one material to the other. 
Dry ice crystals sliding along the metallic wing of an 
aircraft communicate large amounts of negative elec- 
tricity to the aircraft and positive electricity to the ice 
crystal. It is well known that snow blowing along the 
ground acquires a strong negative charge which is very 
likely of similar frictional origin. 

One of the important basic processes that produce 
electrical effects in the atmosphere results from the 
chemical adsorption of ions at the surfaces of precipi- 
tation particles. Systematic polarization and orienta- 
tion of surface molecules frequently result. This orien- 
tation produces electrical double layers that are 
responsible for electrophoresis and a number of aflied 
surface phenomena [9]. In pure water the polarization 
of the surface molecules is such that the outer surface 
is made up of negative charges, Avhile some 10~^ cm 
below this negative surface a positive distribution of 



PRECIPITATION ELECTRICITY 



131 



exactly the same amount of electricity exists. Inside 
this double layer, a more or less random distribution of 
both positive and negative free charges is re-estab- 
lished. The net result of the double layer on the surface 
of a spherical drop is that the potential inside the drop 
may be greater than that outside by a fraction of a 
volt. This does not mean that free electrification is pro- 
duced, since it must be remembered that exactly equal 
amounts of positive and negative electricity are en- 
compassed by the double layer. However, if the double 

' layer is subsequently broken and mechanical work is 
done on it or if ions are selectively captured, measurable 
amounts of free electrification may result. 

One familiar charge-producing mechanism, inti- 
mately related to this double-layer process, is the so- 
called waterfall effect first studied by Lenard [19]. 
Subsequent experimentation has shown that when a 

■ droplet of pure water is broken up by mechanical 
means, the residual droplets carry positive charges 
while the adjacent air acquires both positive and nega- 
tive ions. Electrifications produced by breakup, atomi- 
zation, splashing, or bubbling are all intimately related 
to the double-layer characteristics; this subject has 
received much study [2, 5]. Although one widely quoted 
theory invokes such mechanisms to describe thunder- 
storm electricity, quantitative agreement with obser- 
vation is quite unsatisfactory. 

One aspect of double-layer electrification may be of 
importance in the atmosphere when hail is produced. 
Dinger and Gunn [6] discovered that when water freezes 
in the atmosphere a large amount of air is entrapped in 
the ice in the form of tiny bubbles. Upon melting, 
these bubbles are released, and upon breaking the sur- 
face they transfer to the adjacent air a negative charge 
of 1.25 esu gram""' while the melted water droplet re- 
tains an -equal and opposite positive charge. The free 
charge thus produced is appropriately distributed near 
the freezing level and is sufficiently large to explain the 
presence of active cloud electrification. These experi- 
menters also discovered that the freezing of relatively 
pure water is accompanied by transient changes in the 
contact electromotive force amounting to 6 or 10 v. 

' Because the charge distribution at the surface, respons- 
ible for the contact electromotive force, is in the nature 
of a double layer, they did not believe it contributed to 
a net electrification of a freezing droplet. Using special 
dilute solutions. Workman and Reynolds [29] have re- 
examined this latter process and report that potential 
differences exceeding even 100 v are produced under 
special circumstances. 

It is important to note that the magnitudes of elec- 
trical effects in all double-layer phenomena depend 
critically upon the purity of the water. Banerji [2] has 
remarked that impurities commonly existing in precipi- 
tation in the atmosphere are usually sufficient to reduce 
the expected electrical effects to small values. 

Environmental Processes. It is an observed fact that 
the atmosphere is pervaded by relatively large numbers 
of ions of both signs. The small negative ions move 
10-40 per cent faster than the positive ions when acted 
on by the same force. Therefore, the negative ions usu- 



ally determine the charge captured by an initially un- 
charged and insulated body. 

It has long been known that an insulated conductor 
supported in an ion stream becomes charged due to 
the selective capture of ions. Pauthenier and Moreau- 
Hanot [21] have formulated this process in a quantita- 
tive theory that appears to agree well with experiment. 

Wilson [28] has also pointed out that a droplet fall- 
ing in an electric field is polarized, and as it falls it 
selectively captures, because of its motion, the more 
mobile ions in the volume it sweeps out. Experimental 
results confirm the reality of this process [10]. Since 
this important charge-separating effect depends upon 
the existence of an initial electric field, its application 
to the description of the electrical properties of the 
atmosphere is obscure. The mechanism is useful in 
describing changes in the electrical state subsequent to 
the establishment of an electric field by some more 
fundamental mechanism. 

Electrification occurring when rime is deposited on 
a conducting surface or on graupel is considered im- 
portant by Findeisen [8], who has based a theory upon 
it. The effect is real, but its quantitative relation to 
thunderstorms has not yet been completely worked 
out. The application of this mechanism is attractive 
because it correlates the observed high electrification 
occurring near the freezing level with theory. 

An environmental process first investigated by Gunn 
[13] depends on the differential migration of atmos- 
pheric positive and negative ions under the influence 
of a systematic transfer of water molecules. He showed 
that the transfer of water vapor towards a condensing 
droplet results in a transfer of momentum to both the 
positive and negative ions in the vicinity and the es- 
tablishment of a greater concentration of the most 
mobile ion adjacent to and upon the condensing drop- 
let. The charge capable of being transferred to such a 
droplet is related to the vapor stream \'elocity and to 
the thermal kinetic energy of the molecules, and hence 
in the atmosphere is something less than 0.1 v. It 
should be clear that reversing the direction of the water- 
vapor stream will reverse the sign of the charge on the 
evaporating or condensing droplet. 

Association Processes. In attempting to understand 
the basic mechanisms responsible for the surprisingly 
large electrical charge sometimes carried by precipita- 
tion, one process should be emphasized. Without dis- 
cussing the details of association, it seems certain that 
rain produced below the freezing level results from the 
association of an extremely large number of cloud 
particles. In typical cases, the number of cloud particles 
associated to produce a single raindrop is surprisingly 
large, and if any process systematically transfers even 
small charges of a given sign to the cloud particles, then 
the total charge may be large. Gunn [13] worked out a 
complete "association theory" of electrical storm activ- 
ity based on this idea. He remarked that a number of 
physical and chemical forces could be expected to trans- 
fer small charges to the cloud particles. To illustrate 
the theory, he adopted the notion that each cloud 
particle was an electrical concentration cell and that 



132 



ATMOSPHERIC ELECTRICITY 



the mean potential between the droplet and the outside 
air approached 60 mv. By estimating the total charge 
resulting from the association of typical cloud elements, 
relatively large free charges per droplet were calcu- 
lated. It was found that precipitation electrical phenom- 
ena could be well described, both qualitatively and 
quantitatively, by such an hypothesis. The theory is 
not considered complete but it does serve to emphasize 
the probable importance of association mechanisms 
in the production of highly charged precipitation. 

Separation of Free Electrical Charges and the Impor- 
tance of Droplet Size 

Although all matter is composed of an enormous 
number of electrical charges, it is a general rule that 
e\'erjr email volume of space contains as manj^ positive 
charges as negative charges. A short calculation will 
show that this indeed must be the case, because any 
systematic separation of charges of opposite sign im- 
mediately sets up surprisingly large electrical forces 
that always act in such a direction as to restore elec- 
trical neutrality. 

An important exception to the general rule of neu- 
trality occurs in the earth's atmosphere when free 
charges of one sign become selectively attached to the 
larger or smaller precipitation elements. As an example, 
suppose that, for some reason, all of the elementary 
cloud particles in a given volume selectively capture a 
positive (or negative) charge. When rain is formed, 
these cloud particles associate to form a highlj' charged 
raindrop. Suppose that, simultaneously, neutralizing 
negative (or positive) charges for each droplet are 
immediately outside and are attached to air molecules 
or other very small molecular aggregates. Gravity acts 
on both types of charged carrier, and they fall at a 
velocity determined by the acting aerodynamic and 
electrical forces. When the droplets are small, so that 
gravity does not give the particles high velocities, the 
neutralizing negative (or positive) charges are carried 
along with the falling positive (or negative) droplets 
as a result of electric fields. Thus, after a preliminary 
small separation, gross separations of the type ob- 
served in thunderstorms do not result. 

Unfortunately, the literature does not contain an 
adequate discussion of the important problem of charge 
separation as influenced by the size of the droplet. 
Since the droplet size and the acting forces are of the 
utmost importance in understanding charge separation 
and lightning processes in the atmosphere, it has seemed 
worth while to discuss this matter here. 

Consider a cloud of infinite extent, lying parallel to 
the earth's surface and composed of but two types of 
particles: (1) raindrops upon which positive charge, for 
example, is selectively deposited; (2) particles (as- 
sumed to be small) with a sufficient number of them 
carrying a total charge just large enough to neutralize 
the positive charge on the rain droplets. Assume, at 
first, that the whole cloud system contains exactly as 
much positive electricity as negative, each uniformly 
distributed. It will therefore be neutral and no electric 
fields will exist. 



It is noted first that an electric field produced by 
the separation of charges always acts in such a direc- 
tion as to prevent the separation. Thus, if positively 
charged droplets fall with respect to negatively charged 
droplets, the electric field thus produced acts to support 
raindrops while simultaneously it drags the small nega- 
tive elements downward. 

It is clear that the electric field can never grow to 
exceed a value greater than that of the field which will 
support the droplet. Thus, if E^ is the electric field 
when the droplets are completely supported by it, q is 
the charge on the droplet and m is its mass, while g is 
the acceleration due to gravity, one may equate the 
electrical and gravitational forces and write 



Em = 



mg 



(1) 



This electric field is an absolute maximum in the at- 
mosphere for droplets of a given size and is large 
enough in general to cause spark discharges. 

The equilibrium electric field Em, described above, is 
never realized practically because of the conductivity 
of the earth's atmosphere, which always acts to dis- 
charge and reduce any electric field so produced. In 
order that one may formulate quantitatively the actual 
equilibrium when the droplets are allowed to fall in an 
electricall}^ conducting atmosphere, a one-dimensional 
solution will be obtained by considering the transfer of 
charge within a prism one square centimeter in cross 
section and extending vertically through the cloud. The 
electric current per unit area, i, due to the convected 
charges on the precipitation, is 



= Z) in+q+v+ + n-q-v-), 



(2) 



where n is the number of charged particles per unit 
volume, q the charge on each particle, and v the veloc- 
ity of fall, and where the subscripts denote the sign of 
the transported charge. This downwardly transported 
net free charge per unit time, i, not only charges the 
conducting earth below but also supplies charge to re- 
place that conducted upward as a result of the normal 
ionic conductivity of the atmosphere and the generated 
electric field. If Q is the total free charge per unit area 
deposited on the surface of the earth, then, equating 
the rate of supply to the rate of loss of charge, one has 

-^ + (tE = Y, {n+q+v+ + n_q_vJ), (3) 

where a is the normal ionic conductivity of the earth's 
atmosphere, and E is the electric field generated by 
the charge separation. Under the assumed geometrical 
conditions, the surface charge density Q is related to 
the produced electric field E by the relation 



E = 4tQ, 



(4) 



from which one may write, for regions near the earth's 
surface, that 

— -^-1- aS = X) (■>i'+q+v+ + n^q-v-). (5) 



PRECIPITATION ELECTRICITY 



133 



Before integration of this expression is possible, the 
distributions and the velocities of fall must be ex- 
pressed as a function of the gravitational forces and 
electric field. Under most conditions, the velocity of 
fall may be determined from the terminal velocity of 
fall of a spherical body in the earth's gravitational 
field together with known values for the electric field 
and the mobility of the particle. The terminal velocity 
of fall, V, for droplets of various sizes has been accu- 
rately determined and may be read from tables [6]. 
The mobility u is defined as the velocity of the particle 
in unit electric field, whence one may write approxi- 
mately 



y = V + UE. 



(6) 



Thus, droplets carrying charges of one sign move faster 
than their normal terminal velocity, while those of op- 
posite sign move slower. Substituting this approxima- 
tion in (5), assuming that the droplets are all the same, 
and integrating, one finds that the electric field in- 
creases with the time t in accordance with the following 
relation, 



n+q+V. 



E 



1 + 



n+q+V+_ 



a — ri-q-U. 
[1 -e 



1 + 



n+q+u+ 



(7) 



-47r[(T— n_Q_«_(H-(n+ff^u.|.)/(n_Q_u_))] t-i 



whence, approximating, the maximum equilibrium field 
is given nearly enough by 



E 



n+q+(V+ - V-) 
a + Ti-q-U- 



(8) 



where all quantities are now expressed as positive num- 
bers. Attention is dra^vn to the fact that the selection 
of signs given above is arbitrary, and that in nature a 
negative instead of a positive charge frequently comes 
down on rain. 

In interpreting equation (7), it is noted that when 
the positive carriers are small and have very low ter- 
minal velocities of fall, their actual velocities closely 
approximate the velocities of the carriers of negative 
charges. Thus the difference in terminal velocities be- 
comes small, and the electric field approaches zero. In 
nonprecipitating clouds, therefore, one would expect 
that the measured electric fields would be very small; 
this is in accordance with direct observation [16]. When 
the rain droplets become reasonably large, the electric 
fields increase to large values. In fact, according to 
equation (7), the electric field is proportional to the 
rainfall intensity and to the free electric charge carried 
by the larger droplets. Since the negative carriers are 
very small compared to a raindrop, one may ignore 
their velocity and calculate Table II from equations 
(1) and (8), using the best available data [13, p. 94] to 
show how the eciuilibrium electric field increases with 
the size of the raindrop. It is interesting to note in 
Table II that, while cloud droplets produce a negligible 
field, the equilibrium field for large droplets is great 



enough to produce a discharge in air and thus initiate 
lightning. Equation (8) is therefore consistent with 
observation. 

Using balloons, Simpson and Robinson [26] made 
measurements purporting to show that the electric 
fields inside active electrical storm clouds are "of the 
order of 100 volts/cm." This conclusion is seriously in 
error, for actual measurements in aircraft show that 
fields of 1000 V cm"' commonly occur in such clouds 
without producing a lightning stroke [16]. The electric 
field on the belly of a B-25 aircraft at the beginning of 
an energetic lightning stroke has been measured as 
3400 V cm-i [14]. 

Table II. Electric Field and Dkoplet Size 



Fog 

Drizzle 

Medium rain. . , 
Excessive rain . 



Droplet radius 
(cm) 


5 X 10-" 
1 X 10-2 
5 X 10-2 
1 X 10-1 



Electric field to 
support droplet, 

(v cm"') 



1,500 

24,000* 
24,000* 
24,000* 



Maximum 
equilibrium electric 

field {v cm'') 



0.5 

10.8 
1,930 
24,300* 



* Because the effective dielectric strength for long discharge 
paths in air approximates only 3000 v cm-', active lightning 
strokes would prevent such high values of electric field from 
maturing. 

From equation (7) it can correctly be inferred that 
an increase in the conductivity of the atmosphere will 
reduce the generated electric field. It is not impossible 
that sudden localized increases in the electrical conduc- 
tivity of the air, due to a lightning discharge or local- 
ized radioactivity, would so increase the conductivity 
that the generated electric fields would be small even 
with large droplets and big free charges. Thus, light- 
ning would be suppressed. This matter requires further 
investigation and may be of importance in the artificial 
suppression of lightning discharges by localized dissi- 
pation of radioactive material into the atmosphere. 

The analysis presented above properly emphasizes 
the dual and interrelated character of thunderstorm 
electricity as compared with charge production and 
separation. Electric storm fields would not exist if 
charges were not actively separated. The analysis shows 
that separation cannot take place unless the forces 
acting on the positi\'e charges are different from the 
forces acting on the negative charges. This implies, in 
turn, the necessity for a selective deposit of a charge of 
definite sign on rain particles and a deposit of a charge 
of opposite sign on lighter cloud particles or air mole- 
cules. 

Electrification of Aircraft Flying through Precipitation 

It A\'as found during World War II that aircraft fly- 
ing in cold areas systematically lost all radio commu- 
nication and navigational facilities whenever they en- 
countered dry ice-crystal clouds or snow. Pilots flying 
through such precipitation in mountainous areas with- 
out usable radio navigational facilities continually faced 
dangerous situations that adversely affected the deli^'- 
ery of urgent war goods to Alaska. 

Hundreds of flights made by the Army-Navy Pre- 
cipitation-Static Research Team near Minneapolis, 



134 



ATMOSPHERIC ELECTRICITY 



through all kinds of precipitation and under varying 
meteorological conditions, established the basic mech- 
anisms responsible for precipitation static. By using a 
specially instrumented aircraft, it was found that the 
two most important sources of electrification of the 
aircraft were (1) closely adjacent, highly electrified 
cloud centers, and (2) friction of snow and ice crystals 
as they slid over the wings at low temperatures. Ordi- 
nary rain or shower clouds showing little vertical con- 
vection were relatively inactive. 

The Research Team was able to demonstrate that 
the interference with communications on the aircraft 
resulted from St. Elmo's fire or corona discharges from 
the aircraft antenna or closely adjacent structures. 
Because of the intermittent pulselike nature of the 
corona discharge, adjacent radio circuits were strongly 
shock-excited and rendered insensitive to the ordinary 
radio signals. 

Normal thunderstorm activity produces large electric 
fields in the atmosphere; when the plane is in the vicin- 
ity of these fields, corona currents frequently are pro- 
duced on the aircraft. Because an airplane traverses a 
typical electrically active cloud center in a relatively 
short interval of time, this type of disturbance (while 
especially severe) does not persist for long and there- 
fore is not a serious handicap to navigational radio 
communication. The main difficulty arises from the 
fact that lightning sometimes strikes the aircraft or 
that very intense electric fields break down the insu- 
lating wire used on antennas. 

The second type of electrification is self-produced 
by the aircraft as a result of frictional effects of snow 
or ice crystals as they slide over metallic parts of the 
aircraft. In frontal conditions this type of electrification 
may last for hours and, because radio navigational 
facilities must be constantly employed on aircraft, it is 
evident that such continuous electrification constitutes 
a dangerous operational hazard. 

The frictional charge produced on the airplane proper 
when flying in dry snow or ice crystals is always nega- 
tive, while flakes leaving the plane after sliding along 
its surface carry a positive charge. Experimental in- 
vestigations have established the fact that the rate of 
charge production depends on the character of the 
metallic surface intercepting the precipitation. The 
charging increases with snow or ice-crystal density and 
with the cube of the air speed. As one might expect, 
the Research Team found that the charging rate was 
dependent upon the temperature, being relatively small 
near the freezing temperature and increasing as the 
temperature dropped to about — 15C. 

It is impractical to review the detailed effects that 
result from flying through precipitation. Interested 
readers are urged to read the extensive technical re- 
ports of the Precipitation-Static Project [7, 18]. 

As an illustration of the severity of precipitation 
static, it seems worth while to give some numerical 
results obtained off Yakutat, Alaska, in a typical up- 
slope storm. Cloud and charging conditions were singu- 
larly uniform and serious electrification was observed 
for more than three hours. A four-engine B-17 aircraft. 



cruising at 165 mph, generated an average current of 
750 ;ua. This current transferred a negative charge to 
the airplane and raised its potential to more than 450, 
000 V. The electrical energy dissipated, therefore, was 
330 w. It was not surprising that corona discharge 
from the antenna was initiated causing such severe 
radio interference as to override urgently required com- 
munications. ^ 

Precipitation static is still a serious operational haz- 
ard because the present high operating speed of air- 
craft has greatly increased the charging rates that 
were already troublesome at low speed. The modern 
trend toward still higher speeds will ultimately de- 
mand housed antennas for communication purposes. 
Such construction will greatly assist in meeting future 
requirements. 

REFERENCES 

1. Baneeji, S. K., "Does Thunderstorm Rain Play Any Part 

in the Replenishment of the Earth's Negative Charge?" 
Qiiart. J. R. meteor. Soc, 64:293-299 (1938). 

2. "On the Interchange of Electricity between Solids, 

Liquids and Gases in Mechanical Actions." Indian J. 
Phys., 12:409-436 (1938). 

3. and Lble, S. R., "Electric Charges on Raindrops." 

Nature, 130:998-999 (1932). 

4. Chalmers, J. A., and Pasquill, F., "The Electric Charges 

on Single Raindrops and Snowflakes." Proc. phys. Soc. 
Land., 50:1-15 (1938). 

5. Chapman, S., "Mechanisms of Charge Production in 

Thunderclouds." Abstract. Phys. Rev., 68:103 (1945). 

6. Dinger, J. E., and Gdnn, R., "Electrical Effects Associ- 

ated with a Change of State of Water." Terr. Magn. 
atmos. Elect., 51:477-494 (1946). 

7. Edwards, R. C, and Brock, G. W., "Meteorological As- 

pects of Precipitation Static." /. Meteor., 2:205-213 
(1945). 

8. FiNDEisEN, W., "tJber die Entstehung der Gewitterelek- 

trizitat." Meteor. Z., 57:201-215 (1940). 

9. Gilbert, H. W., and Shaw, P. E., "Electrical Charges 

Arising at a Liquid-Gas Interface." Proc. phys. Soc. 
Land., 37:195-213 (1925). 

10. GoTT, J. P., "On the Electric Charge Collected by Water- 

Drops Falling through a Cloud of Electrically Charged 
Particles in a Vertical Electric Field." Proc. roy. Soc, 
(A) 151:665-684 (1935). 

11. GscHWEND, P., "Beobachtungen iiber die elektrischen 

Ladungen einzelner Regentropfen und Schneeflocken." 
Jb. Radioakl., 17:62-79 (1920). 

12. GuNN, R., "The Free Electrical Charge on Thunderstorm 

Rain and Its Relation to Droplet Size." J. geophys. Res., 
54:57-63 (1949). 

13. "The Electricity of Rain and Thunderstorms." Terr. 

Magn. atmos. Elect., 40:79-106 (1935). 

14. "The Electrical Charge on Precipitation at Various 

Altitudes and Its Relation to Thunderstorms . ' ' Phys. Rev., 
71:181-186(1947). 

15. "Free Electrical Charge on Precipitation Inside an 

Active Thunderstorm." J. geophys. Res., 55:171-178 
(1950). 

16. "Electric Field Intensity Inside of Natural Clouds." 

J. appl. Phys., 19:481-484 (1948). 

17. and Kinzer, G. D., "The Terminal Velocity of Fall 

for Water Droplets in Stagnant Air." J. Meteor., 6:243- 
248 (1949). 



PRECIPITATION ELECTRICITY 



135 



18. and others, "Technical Reports on Precipitation 

Static." Proc. Inst. Radio Engrs., N. Y., 34:1S6P-177P; 
234-254 (1046). 

19. Len.'Vrd, P., "tjber Wasserfallelektrizitat und iiber die 

Oberflachenbeschaffenheit der Flussiglceiten." Ann. 
Phijs., Lpz., 47:463-524 (1915). 

20. Nakata, U., and Tehada, T., "On the Electrical Nature 

of Snow Particles." /. Fac. Sci. Hokkaido Univ., 1:181 
(1934) . 

21. Pauthenier, M., et Moheau-Hanot, M., "Controle ex- 

perimental du mouvement de petites spheres m^talliques 
dans un champ ^lectrique ionise." C. R. Acad. Sci., 
Paris, 194:544-546 (1932). 

22. Pearce, D. C, and Cxjrrie, B. W., "Some Qualitative 

Results on the Electrification of Snow." Canad. J. Res., 
27(A) :l-8 (1949). 



23. ScRASE, F. J., "Electricity on Rain." Geophys. Mem., Vol. 

9, No. 75 (1938). 

24. "The Air-Earth Current at Kew Observatory." Geo- 
phys. Mem., Vol. 7, No. 58 (1933). 

25. Simpson, G. C, "Atmospheric Electricity during Dis- 

turbed Weather." Terr. Magn. atmos. Elect., 53:27-33 
(1948). 

26. and Robinson, G. D., "The Distribution of Electri- 
city in Thunderclouds, II." Proc. roy. Soc, (A) 177: 
281-329 (1941). 

27. WiGAND, A., "Ladungsmessungen an natiirliehen Nebel." 

Phys. Z., 27:803-808 (1926). 

28. Wilson, C. T. R., "Some Thundercloud Problems." /. 

Franklin Inst., 208:1-12 (1929). 

29. Workman, E. J., and Reynolds, S. E., "Electrical Phe- 

nomena Resulting from the Freezing of Dilute Aqueous 
Solutions." Abstract. Phys. Rev., 75:347 (1949). 



THE LIGHTNING DISCHARGE 

By J. H. HAGENGUTH 
General Electric Company, Pittsfield, Massachusetts 



The thunderstorm process and the theories relating 
to the formation of charges in the clouds are explained 
in another article.' This paper will contain information 
on the lightning discharge only. 

The mechanism of the lightning discharge can be 
divided into three regions of interest: (1) cloud-to-cloud 
discharges, (2) cloud-to-ground discharges, and (3) phe- 
nomena on the ground end of cloud-to-ground dis- 
charges. From the practical point of view, the greatest 
effort has been devoted to understanding and interpret- 
ing the phenomena associated with the lightning stroke 
when it contacts man-made installations [1, 2]. Quali- 
tative data have been obtained to give confidence in 
the principles of protection used to guard buildings and 
electrical transmission systems against the effects of 
lightning. It becomes progressively more difficult to 
determine the mechanism and physics of the lightning 
stroke as it occurs away from the earth. 

Leaders 

The study of the mechanism of strokes to ground has 
been accomplished primarily by means of photography 
[15, 16]. The lightning stroke starts at the cloud in the 
form of a stepped leader, as illustrated in the upper 
part of Fig. 1. The steps have an average length of 50 
m. The time interval between successive steps is of the 

Table I. Characteristic Data for Leaders 
AND Return Strokes 





Minimum 


Average 


Maximxmi 


Stepped leaders 

Length of steps, m. . . . 

Time interval between 
steps, /xsec 

Velocity of propaga- 
tion of step, cm sec~^ 

Velocity of propaga- 
tion of pilot streamer, 
cm sec~^ 


10 

15 

1 X 10' 


50 

50 
5 X 10» 

1.5 X 10' 


200 
100 

5 X 10' 






Continuous leaders 
Velocity of propaga- 
tion, cm sec~^ 





2 X 108 


_ 


Return stroke 

Velocity of propaga- 
tion, cm sec~^ 


2 X 10« 


5 X 10' 


1.5 X 10i» 



order of 50 ^sec. The average velocity of the individual 
steps is of the order of 5 X 10^ cm sec"', while the 
velocity of the total step mechanism is of the order of 
1.5 X 10^ cm sec^'. Thus, the total time required for 
the stepped leader to reach the earth may be greater 
than 0.01 sec. 



1. Consult "Precipitation Electricity" 
128-135 in this Compendium. 



by R. Gunn, pp. 



After the leader reaches the earth, the photographic 
film shows a much brighter illumination traveling up- 
wards from the earth toward the cloud through the 
channel established by the stepped leader. This is 
called the return stroke. The average velocity of propa- 
gation is 5 X 10' cm sec~^ 

Subsequent to this first discharge there may be other 
discharges. These are also initiated by a leader, but of a 
different type, called dart leader or continuous leader, 
with a velocity of 2 X 10^ cm sec~^ As in the case of 
the first discharge, return strokes result on contact of 
the continuous leader with the earth. Occasionally 
leaders on discharges subsequent to the first have been 
observed to have a few steps. Data on leader and re- 
turn-stroke characteristics are given in Table I. 

Branching 

Frequently the first discharge shows branching pro- 
duced by a stepped-leader process. Branching is always 
in the direction of propagation of the leader. In general, 
subsequent leaders do not show branching, choosing 
the path where ground previously has been reached, 
resulting in a return stroke. In many cases more than 
one branch may reach ground simultaneously. In other 
cases ground is reached at a different point on subse- 
quent discharges, following and completing a branch 
established on the first discharge. Upward branching 
has also been observed at the cloud end of the stroke. 
Photographs show that branching is the result either of 
discharges between portions of the cloud or of discharges 
from a different charge center in the cloud through 
part of the previously established channel. There are 
indications that branching is more profuse in hilly, 
wooded country than in fiat, bare country. 

Theories have been developed to explain the leader 
mechanism [8, 14]. These theories consider the presence 
of a pilot streamer which progresses more or less con- 
tinuously, connecting the individual bright tips of the 
original leader. As the pilot streamer progresses, the 
ionization in the upper part of the streamer slows up 
and recombination of ions occurs. The impedance of the 
path therefore increases, and hence the potential dif- 
ference across the established channel is also increased. 
As the potential is raised, reionization occurs down the 
channel. The speed and intensity of ionization increase 
as ionization reaches the tip of the pilot streamer. This 
increases the energy at the tip and results in greater 
illumination. The pilot streamer then proceeds for an- 
other 50 m and the process is repeated. 

The breakdown or ionization process begins in a part 
of the cloud characterized by a high field gradient. At 
atmospheric pressure, 30,000 v cm~' are required to 
begin ionization. At the reduced pressure in the clouds 



136 



THE LIGHTNING DISCHARGE 



137 



and due to the presence of water droplets, it is esti- 
mated that a gradient of 10,000 v cm~' may be sufficient. 
Tlie process is started by the acceleration of one or more 
free electrons in the air. By collision with air molecules, 
these electrons liberate more and more electrons as they 
advance in the field, the number increasing very rapidly 
in the form of an avalanche. Large numbers of positive 
ions are left behind in the field. The resulting positive 
space charge increases the field gradient sufficiently 
for the attraction of photoelectrons. These in turn 
produce greater ionization and rapidly complete the 
breakdown process. 



ten to several hundred feet. However, the evidence is 
insufficient to determine whether ground streamers oc- 
cur on every lightning discharge. 

If light intensity is considered a measure of the 
current amplitude in the return stroke, then in the 
majority of the cases photographed the first in a series 
of multiple strokes appears to carry current of the 
highest amplitude. This is not always the case. Oscillo- 
graphic evidence also indicates that the first current 
peak does not always have the highest amphtude. 

In many photographs taken in South Africa [9], 
the light intensity of the channel decreases as the 




STILL CAMERA 
PHOTOGRAPH 
OF STROKE 



INITIAL DOWNWARD 
STEPPED LEADER 



RETURN 
STROKE 



SUBSEQUENT DISCHARGES WITH DOWNWARD 
CONTINUOUS LEADERS 



HIGH SPEED BOYS CAMERA PHOTOGRAPH OF THE SAME STROKE 
CLOUD TO EARTH 




STILL CAMERA 
PHOTOGRAPH 
OF STROKE 



BRIGHT TIPS OF 
LEADER STROKE 




INITIAL UPWARD 
STEPPED LEADER 



'RETURN 
STROKE 



SUBSEQUENT DISCHARGES WITH DOWNWARD 
CONTINUOUS LEADERS 



HIGH SPEED SOYS CAMERA PHOTOGRAPH OF THE SAME STROKE 
CLOUD TO TALL CONDUCTING STRUCTURE 



Fig 1. — Schematic diagram showing the mechanism of the lightning discharge from cloud to ground. 



Laboratory experiments on long sparks have con- 
firmed the stepped-leader process from negative point 
to plane, but not from positive point to plane. More 
sensitive measuring methods are needed to record the 
complete development of the streamers or leaders. There 
is considerable doubt as to the existence of the pilot 
streamer. The theory of the long discharge is not yet 
sufficiently developed, however, to provide a better 
answer to the formation of the lightning stroke by 
means of the stepped leader. 

The Return Stroke 

As the leader approaches the ground, the charges 
in the ground begin to move in the direction of the 
approaching leader. As the leader touches the ground, 
the charges in the channel and the ground charges 
can neutralize each other, resulting in the return stroke. 
Since the channel is partly ionized, further ionization 
can result at a more rapid rate. The current in the chan- 
nel increases rapidly and the velocitj' of propagation 
upward becomes of the order of ten times that of the 
continuous downward leader. 

There is some evidence that streamers from the 
ground start up toward the approaching leader, thus 
producing contact between leader and charges in the 
air [11]. The length of such streamers may vary from 



I'cturn stroke progresses toward the cloud. Points of 
discontinuity are observed, particularly at the junctions 
of the main channel and the branches. There is a ques- 
tion of whether current surges proceed from the branch 
to ground or from the ground to the branch. The veloc- 
itj^ in most cases exceeds 10'" cm sec~', and therefore 
cannot be accurately measured from the photographs. 
Measurements in other parts of the world do not seem 
to indicate such drastic changes in intensity in the 
channel as the return stroke progresses toward the 
cloud. This difference may be due to ground conditions. 
In those cases where charges are readily available, the 
current in the return stroke can be maintained up to 
higher altitudes at higher amphtudes than in ground 
with high resistivity. 

Data are not available on current amplitudes in the 
leader strokes, the relation between ciu'rents and charges 
in the leader stroke, the charges available in the ground, 
and the wave shape and amplitude of the return stroke. 
The mechanism in^^olved in the wave shape of the 
current in the return stroke is not too clear. It is thought 
by some that the front is formed shortly before the 
leader touches the ground and completed on contact 
[12]. Other theories indicate that maximum peak cur- 
rent is reached at the ground end after the current 
wave has traveled a short distance upwards in the 
channel. 



138 



ATMOSPHERIC ELECTRICITY 



Stroke Mechanism for High Buildings 

Observations at the Empire State Building in New 
York [11] have shown that the starting mechanism of 
the stepped leader is quite different (bottom part of 
Fig. 1). In most cases the stroke starts as a stepped 
leader at the building rather than at the cloud. The 
length of the steps, the time interval between steps, 
and the velocity of propagation of the steps fall within 
the range of leaders from cloud to ground. Another 
significant difference is the absence of a return stroke 
after the leader has reached the cloud. Instead, a 
continuous flow of current of the order of magnitude of 
a few hundred amperes is observed. Frequently the 
stroke current stops without any further manifesta- 
tion. In many cases, however, the initial discharge is 
followed by subsequent continuous downward leaders 
from the cloud to the building, followed by a return 
stroke upward from the building, as in the case of 
strokes reaching the ground in open country. 

This sequence leads to the conclusion that charges 
in the cloud are not sufficiently concentrated to provide 
a return stroke. In spite of the large drainage of charges 
(as much as 80 coulombs) in the preliminary continu- 
ous-current period and a rather well-ionized channel, 
the cloud can precipitate a continuous leader to the 
building. This may be due to a more rapid increase of 
potential gradients within the cloud or to rapid inter- 
change of charges from other charge centers within the 
cloud. The reason for establishing a continuous leader 
in a channel, quite well ionized by the preceding con- 
tinuing current, is not clear. Photographs and oscillo- 
grams show that the return stroke, coupled with a 
hea^ry current discharge or peak current, is governed 
principally by conditions in the ground. 

Continuous Current 

Oscillographic and photographic evidence from the 
Empire State Building investigation seems to indicate 
that successive discharges are always connected by 
continuing current flow. Other investigators have made 
measurements which indicate that the current between 
successive discharges may drop to zero. The fact that 
successive lightning discharges in a stroke have the 
same shape is an indication that sufficient ionization 
remains in the channel for subsequent leaders to choose 
the same path. In some cases the time interval between 
such successive discharges is 0.5 sec. In the laboratory 
it was found that on establishing a long, sixty-cycle 
arc, a series of multiple discharges take place within a 
few hundreds of microseconds. The shape of these 
discharges differs greatly, indicating that ionization 
has ceased. The currents available in this case are of 
the order of a few amperes. 

To solve this question it is necessary to greatly en- 
large our knowledge on deionization time of the air and 
to determine more accurately whether current flow 
exists during deionization. 

The Chaimel of the Lightning Stroke 

The channel of the lightning stroke almost invariably 
follows an irregular path. This path and its branches 



are probably determined by the conditions in the atmos- 
phere surrounding the tips of the stepped leaders as 
they progress downward. Space charges produced by 
the leader mechanism, and perhaps charge distributions 
involved in the thunderstorm process itself, may be 
largely responsible for the field distortion resulting in 
the irregular pattern of the lightning channel. The 
diameter of the channel is apparently a function of the 
rate of rise of current flowing in the channel and the 
amplitude of current flow. Experiments have shown 
that the channel diameter experiences equilibrium when 
the density of the current flowing reaches 1000 amp 
cm~^. Much greater current densities, as high as 30,000 
amp cm~-, are reached when current flowing in the 
channel has a rate of rise of a few thousand amperes 
per /isec. As the result of such measurements, the 
probable maximum diameter of the channel was 
deduced as of the order of 5 cm. Other computations 
and experiments indicate diameters as high as 23 em. 

The change in current density and consequent en- 
largement of the channel as a result of ionization, heat- 
ing, and disassociation along the path of the lightning 
discharge, results in pressure effects. For continuous 
discharges involving only low currents, the pressure 
effects are so negligible that thunder cannot be heard. 
Such observations permit the deduction that pressure 
effects will be greater the higher the rate of rise of cur- 
rent flowing in the channel and the greater the ampli- 
tude of the current. This is confirmed by laboratory 
experiments where the pressure effects are associated 
with high surge currents, while low-current discharges 
produce negligible pressure. 

At times the path of the lightning channel is affected 
by wind. In such cases a stationary camera film and 
lens will record the multiplicity of the discharge. In 
some such cases the stroke path changes its shape 
considerably, indicating perhaps the disruption of cur- 
rent flow. However, it is quite possible that differences 
in wind velocity at various heights are responsible for 
distortion of the pre-established channel. In other cases 
the channel retains its precise form to the end of the 
stroke. 

The Multiple Stroke 

The formation of multiple strokes [6, 11] has been 
explained as the extension of the stroke channel to 
new charge centers in other portions of the cloud. 
Alternatively, it has been suggested that new charge 
centers develop toward the original channel by means 
of the leader process. In some strokes the regularity 
of the time interval between successive discharges has 
been suggested to be due to repeated charging of the 
original stroke center. Statistical data on the number 
of multiple discharges in a stroke are given in Table II. 

Potential Involved in the Stroke Formation 

Based on potential gradients measured at the earth 
and within clouds, it now appears that a lightning dis- 
charge can be initiated and completed with average 
gradients of the order of 100 v cm-^ On this basis the 
total voltage required to initiate a stroke of 10,000-ft 



THE LIGHTNING DISCHARGE 



139 



length has been estimated at twenty to thirty miUion 
volts. Considering the formation of the channel by 
means of the stepped-leader process, it is reasonable to 
assume that the average gradient for the lightning 
stroke may be considerably less than that required to 
break down a gap in the laboratory (30,000 v cm"', 
uniform field; 5000 v cm"', nonuniform field — large 
gaps). 

It is not known what gradients exist at the point 
where the leader is initiated in the cloud. The lower 
density of the air, and the presence of waterdrops 
with their associated charges, may greatly alter the 
gradient requirements initiating a discharge. 

Cloud-to-Cloud Discharges 

While the occurrence of cloud-to-cloud discharges 
is relatively much greater than that of cloud-to-ground 
discharges — estimates range between 50:1 and 0.7:1 — 
the mechanism involved is not as well known because 
these strokes are frequently obscured by the cloud 
masses. However, the available photographs seem to 
indicate that cloud-to-cloud discharges are initiated 
by stepped leaders in the same manner as that of the 
first discharge in a cloud-to-ground stroke. Return 
strokes are not known to occur. 

Measurements of field changes associated with cloud- 
to-cloud strokes also indicate the absence of return 
strokes. The measurement of the wave form of atmos- 
pherics, however, has disclosed that some types of 
cloud-to-cloud strokes result in wave forms similar to 
cloud-to-ground strokes, but of smaller 'amplitude and 
separated by short, quiet intervals. These probably 
arise from multiple discharges within the clouds. Photo- 
graphic evidence indicates that discharges within clouds 
can take place from the tip to the bottom of the cloud, 
as well as in a horizontal direction within clouds. 

The importance of cloud strokes lies in their effects 
on radio reception and on the safety of airplanes. It 
has been suggested that airplanes may trigger off cloud- 
to-cloud discharges, and evidence is accumulating that 
the susceptibility of planes to lightning strokes increases 
as the size and speed of the planes become greater. 

Phenomena on Ground End of Cloud-to-Groimd Dis- 
charges 

To safeguard electrical installations against damage 
from lightning strokes, a large number of measurements 
have been made to determine the characteristics of 
lightning strokes at the ground end. Such measurements 
have involved the determination of voltages on trans- 
mission lines (maximum measured — 5,000,000 v), but 
have dealt principally with the statistical evaluation 
of the current in the stroke, the charges involved in 
the stroke, the wave shapes of currents, and other data 
needed to provide reliable protective systems. 

Figure 2 shows a composite oscillogram of a lightning 
stroke current to the Empire State Building. In this 
case an upward leader, followed by a long period of 
continuing current flow, initiated the stroke and ter- 
minated at 0.25 sec. At this moment a continuous 
downward leader to the building resulted in a return 



stroke or current peak of approximately 15,000 amp 
in which the time to half value of the crest current 
was roughly 40 ^sec. A short period of continuing cur- 
rent was followed by a second current peak of 4000 amp. 
A total of four current peaks were measured in this 
stroke, the third one having the highest amplitude, 
23,000 amp. The total duration of the stroke was ap- 
proximately 0.46 sec. 

TIME IN SECONDS 
(INSERT SCALE - MICROSECONDS) 



-2 J 
0.08 



tr -I 

uj 

fe -2 



I u sec. ( / /J sec. ( 

Vo 20 40 60 « 0.26rO 20 . 40 X 





0.320^ -B- ^3„. ♦/-0.320 + 
">0 20 40 60 



;p 



TOTAL DURATION: 0.47 SECONDS 
TOTAL CHARGE: - 84 COULOMBS 



Fig 2. — Replot of low-speed cathode-ray oscillogram with 
inserts of high-speed cathode-ray oscillograms showing cur- 
rent peaks, Empire State Building, New York City, 1940. 

In strokes to open country, the stroke starts at the 
cloud rather than at the ground, and consequently a 
current peak would be the first measurement made. 
The value of continuing current between current peaks 
is expected to vary greatly and may even be zero. Never- 
theless, this oscillogram shows all the principal com- 
ponents of a cloud-to-ground stroke and the relative 
relations between amplitudes and wave shapes of the 
two principal components — current peaks and continu- 
ing currents — as well as the multiple character of the 
stroke. 

From the available measurements, it has been pos- 
sible to derive statistical data which are shown in 
Table II. These statistics in all cases give the minimum 
and maximum curves obtained from published data 
for 90, 50, and 10 per cent of the strokes, as well as 
the maximum available values. The great spread in 
some of the data is due to the various methods of 
observations used. 

Stroke Current 

Item 1 of Table II shows the amplitudes of current 
peaks measured in the path of the lightning stroke, 
with an average peak current of 7000 amp. A much 
greater number of records, which show a surprising 
agreement, have been obtained on transmission line 
towers (Item 2). Fifty per cent of the lower currents 
are in excess of 10,000 amp, while the maximum meas- 



140 



ATMOSPHERIC ELECTRICITY 



ured was 130,000 amp. By making various assumptions, 
the lightning stroke currents responsible for tower cur- 
rents measured were deduced as shown in Item 3. 
The correctness of some of these assumptions is ques- 
tionable, and the values shown in the table are probably 



Table II. Characteristics of 


Lightning Strokes 


Item 


Per cent of strok.es with 

values in excess of 
those shown in Table I 


Maxi- 
mum 




90% 


50% 


10% 




1. Current peaks measured 
in stroke path, kiloam- 
peres 


Min. 
Max. 


2.2 
5.0 


6.0 
8.6 


20.0 
27.5 


160 


2. Current amplitudes in 
steel towers, kiloamperes 


Min. 
Max. 


1.0 

5.3 


8.8 
12.2 


28.4 
35.8 


130 


3. Lightning stroke cur- 
rents computed from 
Item 2, kiloamperes 


Min. 
Max. 


2.4 
10.3 


13.3 
40.0 


50.0 
101.0 


220 


4. Rate of rise of stroke 
currents, kiloamperes per 
fisec 


Min. 

Max. 


1.8 
2.4 


8.5 
14.5 


27.5 
35.0 


45 


5. Wave front of stroke 
currents, /xsec 


Min. 
Max. 


0.2 
0.9 


1.0 
2.51 


5.2 
5.5 


10 


6. Wave tail of current 
peaks — time to half 
value, iisec 


Min. 
Max. 


11.6 
26.0 


30.3 

45.5 


78.0 
80.0 


120 


7. Charges in current 
peaks, coulombs 


Min. 
Max. 


0.04 


0.23 


1.03 


5.6 


8. Total stroke charges, 
coulombs 


Min. 
Max. 


2.3 

4.2 


10.4 
22.2 


86.0 
100.0 


165 


9. Total duration of 
strokes, sec 


Min. 
Max. 


0.1 


0.0006 
0.37 


0.2 
0.68 


1.6 


10. Number of current peaks 
in lightning strokes 


Min. 
Max. 


1.0 
1.3 


1.8 
3.0 


4.0 
11.0 


42 


n. Time interval between 
current peaks, sec 


Min. 
Max. 


0.03 


0.02 
0.088 


0.1 
0.18 


0.5 



too high. The statistical evidence indicates, however, 
that only very few lightning strokes will have current 
peaks in excess of 60,000 amp. 

Wave Shape of Current Peaks 

Of great importance for evaluating the effect of 
lead length in lightning protective systems is the knowl- 
edge of the length of the front and the rate of rise of 
current of the current peaks. The number of records 
available is relatively small. However, the data taken 
by different investigators with different means of re- 
cording are in sufficient agreement to allow confidence 
in the results. The limits of wave fronts and rates of 
rise measured indicate that inductive drops are a serious 
consideration. In 50 per cent of the cases the rate of 
rise was 12,000 amp per /usee or greater, which would 
result in approximately a 6000-v drop per foot of 
conductor. 

The duration of the current peaks is of importance 
in estimating or determining the strength of insulation 
subjected to lightning strokes. For practical reasons 
this is usually expressed in terms of microsecond dura- 
tion of the current wave while it rises from zero to 
crest and decays to half value. The statistical evidence 
shows that 50 per cent of the waves have a time to 
half value of approximately 38 Msec or more. 



The charges in the current peak are related by an 
unknown factor to the charges laid down by the leader. 
The charges measured at the ground end of the stroke 
are expected to be lower than those in the leader be- 
cause of losses during the formation of the leader. The 
charges given in the table are based on the integrated 
product of current in amperes and time in seconds, 
using only the portion of the current peak between 
its start and its decrease to half value. In all cases but 
one, the charges thus determined were less than one 
coulomb and resulted from lowering a negative charge 
from the cloud. The maximum value of 5.6 coulombs 
resulted from lowering a positive charge from the cloud. 

The Composite Stroke 

The lightning stroke may consist of a number of 
current peaks and continuing current flow. The total 
duration of the stroke measured by different investi- 
gators varies between 0.0006 sec and 0.35 sec for the 
50 per cent level. The longest duration measured is 
about 1.5 sec. Fifty per cent of the strokes have two 
or more current peaks, while a maximum of 42 current 
peaks has been measured. The time interval between 
successive current peaks at the 50 per cent level varies 
between 0.02 sec and 0.09 sec, with a maximum of 0.5 
sec between successive discharges. 

Of considerable interest is the total charge in the 
lightning stroke. This is principally the charge conducted 
by the continuous currents. The average charge meas- 
ured is approximately 18 coulombs, while a maximum of 
165 coulombs has been recorded. Many of these meas- 
urements were obtained from strokes to tall buildings, 
and in all cases they represent the charges at the ground 
end of the stroke. They represent the total charges 
conducted in the channel through the point of measure- 
ment. There should be some difference in the total 
charges conducted when the stroke is initiated at the 
cloud and when it is initiated at a tall structure. In 
the latter case, the total charge in the channel can be 
measured, while for strokes initiated at the cloud, 
charges laid down from the cloud are not necessarily 
included in the measurement. 

Measurement at the ground end of the stroke will 
not necessarily record all charges involved in a light- 
ning stroke, particularly in the not-too-rare cases where 
the stroke changes its path at the ground end or at 
both ends. It is obvious that in such cases the total 
charges involved in the stroke mechanism can be con- 
siderably greater. 

Charge determination by means of electric field meas- 
urements of thunderstorms has indicated a maximum 
charge of 200 coulombs, a value about 25 per cent 
higher than at the Empire State Building. A further 
indication of total charges involved in lightning strokes 
has been obtained from damage produced by lightning 
strokes on metal parts, particularly of airplanes. Com- 
parison of such damage with similar effects produced 
in the laboratory has indicated charges at least as high 
as 300 coulombs, and possibly in excess of 500 coulombs. 
In some of these high total charges, strokes to ground 
were also involved, but since the total stroke mecha- 



THE LIGHTNING DISCHARGE 



141 



nism is not kno^vn, it cannot be determined whether 
all of the charges were conducted to ground or to what 
extent they occvu-red within the cloud only. 

Polarity 

The polarity of lightning strokes, in the great ma- 
jority of cases measured, is negative; that is, negative 
charges are lowered from the cloud. The relation for 
grounded structures is approximately 15:1 in favor of 
negative charges. Since most measurements have been 
made on transmission line towers and other rather 
well-grounded structures, it has been pointed out that 
this would be conducive to a higher number of negative 
strokes on account of the possibility of guiding a nega- 
tive leader to the structure by means of streamers 
produced at the positive grounded object. In the case 
of a positive stroke, a negative streamer would not be as 
likely to occur. From this reasoning it is expected that 
strokes to open ground may include a lower percentage 
with negative polarity. Measurements of field changes 
seem to favor this view because in many of these cases 
the ratio of negative to positive polarity cloud-to- 
ground strokes is of the order of 6: 1 or less. 

In cases where direct strokes to grovmd have been 
measured by means of oscillographs or other devices 
which permit detailed examination of the stroke cur- 
rent throughout its duration, it was found that the 
majority of the strokes were entirely of negative po- 
larity. In some cases, however, the polarity of the 
continuing current flow changed, usually toward the 
end of the stroke. In other cases one of the current 
peaks was of positive polarity, while the remaining 
current peaks resulted from a negative cloud charge. 
The polarity relations throughout the length of the 
stroke are probably governed by the mechanism of 
multiple discharges which was discussed previously. 
The process must be governed by the means of charge 
exchange within the cloud during and following the 
first leader stroke to ground, as well as by the rate of 
production of charges within the original stroke center 
in the cloud. 

The fact that charges of negative polarity are lowered 
to the ground in the majority of the cases seems to 
indicate that negative charges predominate in the bot- 
tom of the cloud. The fact that some of the highest 
current peaks measured were of positive polarity might 
be accepted as proof that centers of positive polarity 
can exist in the lower portions of some storm clouds. 

Stroke Density 

It is extremely difficult to obtain information on 
stroke density. Analysis has shown that the density 
per square mile is approximately one-half of the number 
of storm days from the isokeraunic map. This was 
partially confirmed by a two-year count in a region 
with 27 storm days per year where the average stroke 
density was approximately 15 strokes per square mile 
per year. Observed figures depend on the size of the 
area under observation and rapidly decrease with in- 
creased area. Accurate data would be of value to de- 
termine lightning risks. 



Forms of Lightning 

Names like streak, bead, ribbon, fork, heat, sheet, and 
ball lightning have been used to describe various ob- 
served forms of lightning discharges. Streak lightning 
is the normally observed type as described in the fore- 
going discussion. Bead, ribbon, fork, and heat lightning 
probably have the same characteristics as streak light- 
ning. Bead lightning is assumed to be a form of streak 
lightning. The appearance of the beads may be caused 
by variations in the luminosity along the channel, 
perhaps caused by brush discharges. Ribbon lightning 
is probably a streak lightning stroke with multiple 
discharges where the channel is blown along by the 
wind. Fork lightning is the term used for strokes with 
several apparently simultaneous paths to ground. As 
explained, these ground termini may be formed simul- 
taneously or during successive discharges of multiple 
strokes. Heat lightning is a form of streak lightning 
at a distance sufficiently far away so that thunder is 
not heard. Sheet lightning usually occurs in clouds 
between the lower and upper atmosphere over a con- 
siderable area. This areal distribution of sheet lightning, 
and its long persistence, constitute the principal differ- 
ence between it and streak lightning. 

Ball lightning is described as a luminous ball of 
reddish color, with an average diameter of 20 cm. When 
seen emerging from the cloud, its velocity has been 
estimated as high as 100 m sec"'; while on the ground 
it travels at 1 to 2 m sec~'. Usually the ball explodes 
after an average life of 3 to 5 sec. There is much con- 
troversy regarding this form of lightning. It has been 
described as an optical illusion caused by retention of 
vision of a heavy lightning discharge in the retina of 
the eye. However, the testimony of a few apparently 
well-qualified observers seems to indicate that such 
phenomena may exist. No reliable explanation for the 
existence of ball lightning has been offered. However, 
several theories exist explaining the phenomenon on the 
basis of chemical and physical reactions. Some photo- 
graphic evidence submitted as possibly caused by ball 
lightning has been proved to have had an erroneous 
interpretation. 

Measurements of Lightning Characteristics 

The most exact measurements can be made at the 
ground end of a stroke. For this purpose a variety of 
instruments have been developed. 

The Lichtenberg figure on photographic film [7, 13] 
placed between two electrodes is a corona discharge. 
The size of the figure is a measure of the voltage applied 
and the polarity of the discharge. By suitable shunts, 
currents can be measured. The accuracy of such de\nces 
has been estimated at 25 to 50 per cent. 

A very simple method of measuring the peak value 
and polarity of surge or lightning currents is the mag- 
netic link [4]. It consists of a number of steel strips of 
high retentivity. The magnetic flux associated with a 
lightning stroke magnetizes the link. The magnetization 
measured after exposure gives a very accurate indication 
of current crest. Two links at different spacing from 



142 



ATMOSPHERIC ELECTRICITY 



the conductor carrying the lightning surge are used to 
increase the accuracy, particularly where currents of 
opposite polarity may flow. These links will measure 
only the maximum peak in a multiple stroke. 

Fulchronographs [17], devices where a niunber of 
links are mounted on a rotating wheel, permit deter- 
mination of the variation of current with time. The 
resolution for continuing currents is good. The high- 
speed wheels used permit separation of amplitudes of 
successive high current peaks, but the speed is insuffi- 
cient to determine the wave shapes of current peaks. 

Magnetic links applied in circuits in which induct- 
ances or capacitances are used in combination with 
resistance permit determination of the maximum rate 
of current change of a current peak. 

The photographic surge-current recorder [10] meas- 
ures the intensity of light produced by a surge current 
across a short spark gap. A range of 0.1 amp to 150,000 
amp is claimed for this device. 

The cathode-ray oscillograph [3] is the most versatile, 
but also the most elaborate device for measuring surges. 
Several types of oscillograph must be used to record 
the high-speed (current peaks) and slow-speed (con- 
tinuing currents) components of a complete lightning 
stroke. The development of the sealed-in cathode-ray 
tube has made this instrument simpler and subject to 
automatic operation. 

Of considerable value for determining the mechanism 
of the discharge are the so-called Boys cameras [5, 15]. 
With high-speed rotating film, or high-speed rotating 
lenses, the speed of propagation of the leaders and 
return strokes can be analyzed. The low-speed cameras 
give valuable information on the time sequence of 
current peaks and the continuing-current flow between 
multiple discharges. It has been possible to obtain fairly 
good correlation between density of the film exposed to 
a stroke and the current flow causing the illumination, 
principalljr for the continuing components. A micro- 
photometer has been used to correlate these quantities. 
For accuracy it is necessary to avoid overexposure of 
the film, as well as to have highest sensitivity for the 
weaker illumination. For this purpose multiple-lens 
cameras are used with apertures varied to cover the 
complete range of exposure expected in a straight-line 
relation. 

Electric field measurements permit investigation of 
lightning-stroke phenomena from the point of view of 
the charges involved. Some of the measurements made 
differentiate the leader, the return stroke, and the 
continuing-discharge portions of strokes. The wave 
shapes of atmospherics and correlation with various 
forms of lightning discharges have been investigated. 
Such measurements have been extended to cover dis- 
tances of hundreds of miles. By using two or more 
instruments, the distance of the source of atmospherics 
can be determined with good accuracy. 

A rather useful means of determining lightning char- 
acteristics is the examination of damage produced by 
lightning. By reproducing similar effects in the labora- 
tory it is possible to determine approximately the 
type of stroke responsible for the damage, as well as 



the amplitude of current peaks and the charge con- 
ducted in the stroke. Damage produced on metal parts 
of airplanes is in many respects the only means by 
which lightning currents occurring in the clouds can be 
determined. 

Lightning Protection 

The statistical knowledge gained over the past fifteen 
to twenty years has largely confirmed the effectiveness 
of a properly installed lightning-rod system (advocated 
by Benjamin Franklin more than 150 years ago) to 
protect ordinary buildings and houses against direct 
strokes. Such systems consist of interconnected air 
terminals mounted on the highest points of the struc- 
ture, and connected to the ground at several points. 
The "Code for Protection Against Lightning" issued 
by the National Bureau of Standards and designated as 
Handbook Hlfl, and the British Code of Practice C. P. 
1:1943 published by the British Standard Institution, 
contain the essential rules to follow for installation, 
materials, size, and other factors essential for an ef- 
fective durable installation. 

For continuity of electrical service to homes, farms, 
and factories, many practices have evolved, based di- 
rectly on the many lightning studies and their results. 
For protection of electrical apparatus, the lightning 
arrester is a commonly accepted device. Such arresters 
have the property of conducting surge currents to 
ground at a reduced voltage. Any system power current 
(follow current) which may flow through the arrester 
immediately following the lightning discharge is in- 
terrupted, and the line is restored to its original con- 
dition. Many different types of arresters are in use. 
In some cases plain gaps are used for protection. These 
cannot limit the voltage applied to the apparatus to 
voltages as low as arresters. After sparkover of the gap 
occurs, circuit power current usually follows and must 
be interrupted by opening a breaker. 

Transmission lines of higher voltage ratings can be 
effectively protected by the use of ground wires prop- 
erly suspended above the transmission wires to inter- 
cept the direct strokes. The lightning currents contact- 
ing the ground wire and the towers to which they are 
connected will raise the tower potential by virtue of 
the resistance of the tower to ground and the current 
in the stroke. To this is added the inductive voltage 
drop caused by the inductance of wire and tower and J 
the rate of rise of current on the current front. By \ 
reducing the ground resistance to less than one ohm 
per 12 kv of circuit voltage, it has been possible to 
reduce outages on circuits of 66 kv and above to an 
extremely low value. Ground resistance can be reduced 
by the use of buried wires — counterpoise — or deeply 
driven ground rods. 

Lower voltage circuits have been made lightning- 
resistant in many cases by the use of wood as insulation 
in addition to the normal porcelain or glass insulators. 
Reclosing circuit breakers are another tool for pre- 
venting circuit outages. These breakers are able to open 
a circuit and reclose it in as little as one-fifth of a second 
by means of suitable relaying. Proper balance between 



THE LIGHTNING DISCHARGE 



143 



circuit breaker duty and protective means for reducing 
the number of flashovers must be considered. 

Conclusions 

The physical phenomena of the lightning discharge 
are not entirely understood. Photographic evidence in- 
dicates a stepped-leader initiation of the stroke fol- 
lowed by a return stroke from its ground terminal. 
Tlieoretical stipulation of a pilot streamer has not been 
proven. 

To complete the understanding of the physical phe- 
nomena involved in lightning discharges, more informa- 
tion is required on these principal questions: 

1. The gradient at the point of origin of the stroke. 

2. Gradient distribution within clouds, as well as 
beneath clouds. 

3. Gradients at the ground end of a stroke. 

4. Existence and character of ground streamers prior 
to stroke contact with the ground. 

5. Ionization processes within the stepped leader, 
continuous leader, and the return stroke. 

6. Ionization and deionization of the stroke channel 
with special reference to continuing current discharges. 

7. Influence of ground conditions on the return-stroke 
process. 

For further progress on the protection problem, statis- 
tical evidence is desirable on: 

1. The wave shape of lightning stroke currents of 
both current peaks and continuing currents. 

2. The distribution of such currents in the ground 
network of protective installations, as well as in the 
earth. 

3. The lightning stroke density in various regions of 
the earth. 

4. The incidence of lightning to various structures as 
determined by height and physical location with regard 
to other structures and natural terrain. 

From the numerous investigations of lightning under- 
taken during the last twenty-five years, it has been 
possible to devise protective systems and practices 
which reduce damage due to lightning to a negligible 
factor on electrical installations as well as on buildings. 

REFERENCES 

The sources of information are extensive. References to 750 
papers are found in [1] and [2] below. To keep the number of 
references at a reasonable figure, only a few additional refer- 
ences are listed. 



1. A.I.E.E. Lightning Reference Book, 1918-1935. New York, 

American Institute of Electrical Engineers, 1937. 

2. A.I.E.E. Lightning Reference Bihliographij , 1936-1949. New 

York, American Institute of Electi-ical Engineers, 1950. 

3. Flowers, J. W., "The Direct Measurement of Lightning 

Current." /. Franklin Inst., 232: 425-450 (1941). 

4. FousT, C. M., and Kubhni, H. P., "The Surge-Crest Am- 

meter." Gen. elect. Rev., 35: 644-648 (1932). 

5. Hagenguth, J. H., "Lightning Recording Instruments." 

Gen. elect. Rev., 43: 195-201, 248-255 (1940). 

6. Larsen, a., "Photographing Lightning with a Moving 

Camera." Rep. Smithson. Insin., pp. 119-127 (1905). 

7. Lee, E. S., and Foust, C. M., "The Measurement of Surge 

Voltages on Transmission Lines Due to Lightning." 
Trans. Amer. Inst, elect. Engrs., 46: .339-356 (1927). 

8. LoEB, L. B., and Meek, J. M., "The Mechanism of Spark 

Discharge in Air at Atmospheric Pressure." /. appl. 
Phys., 11: 438^47, 459^74 (1940). 

9. Malan, D. J., and Collens, H., "Progressive Lightning, 

III." Proc. ray. Soc, (A) 162: 175-203 (1937). 

10. McCann, G. D., "The Measurement of Lightning Currents 

in Direct Strokes." Trans. Amer. Inst, elect. Engrs., 63: 
1157-1164 (1944). 

11. McEacheon, K. B., "Lightning to the Empire State Build- 

'ing." /. Franklin Inst., 227: 149-217 (1939). 

12. and McMorris, W. A., "The Lightning Stroke: 

Mechanism of Discharge." Gen. elect. Rev., 39: 487-496 
(1936). 

13. Peters, J. F., "The Klydonograph." Elect. World, N. Y ., 

83: 769-773 (1924). 

14. ScHONLAND, B. F. J., "Progressive Lightning, IV." Proc. 

roy. Soc, (A) 164: 132-150 (1938). 

15. and Collens, H., "Progressive Lightning." Proc. roy. 

Soc, (A) 143: 654-674 (1934). 

16. ScHONLAND, B. F. J., Malan, D. J., and Collens, H., 

"Progressive Lightning, II." Proc. roy. Soc, (A) 162: 
595-625 (1935). 

17. Wagner, C. F., and McCann, G. D., "New Instruments 

for Recording Lightning Currents." Trans. Amer. Inst, 
elect. Engrs., 59: 1061-1068 (1940). 

Further articles containing comprehensive references are: 

18. Bruce, C. E. R., and Golde, R. H., "The Lightning Dis- 

charge." /. Instn. elect. Engrs., 88: 487-505 (1941). 

19. McEachron, K. B., "Lightning and Lightning Protec- 

tion" in Encyclopaedia Britannica, Vol. 14. Chicago, 1948. 
(See pp. 114-116) 

20. and Hagenguth, J. H., "Lightning and the Protection 

of Lines and Structures from Lightning" in Standard 
Handbook for Electrical Engineers, A. E. Knowlton, ed. 
New York, McGraw, 8th ed., 1949. (See pp. 2230-2254) 

21. Meek, J. M., and Perry, F. R., "The Lightning Dis- 
charge" in Reports on Progress in Physics, 10: 314-357. 
Phys. Soc, London, 1944-45. 



INSTRUMENTS AND METHODS FOR THE MEASUREMENT OF 
ATMOSPHERIC ELECTRICITY* 

By H. ISRAEL 
Institute for Atmospheric Electric Research of Buchau a. F. 



System of Units 

Various systems of units are used in electricity. Each 
of these is an entity in itself and is built up on a 
definite fundamental physical relationship: 

1. The "electrostatic cgs system" is based on Cou- 
lomb's law of the force effects of interacting electrical 
charges and arbitrarily takes the proportionality factor 
to be nondiniensional and equal to unity. 

2. The "electromagnetic cgs system" is based on the 
Biot-Savart law of the forces between an electric cur- 
rent and a magnetic pole, and again the proportionality 
factor is set equal to unity. 

3. Giorgi's "natural m-sec-v-amp system" assumes 
voltage and amperage as fundamental quantities, with 
the second (sec) as the time unit and the meter (m) 
as the length unit. 

In the first two systems the electrical quantities are 
reduced to the mechanical units, cm, g, and sec (cgs), 
which appear in complicated, nonvisualizable com- 
binations. The third system of units is more suitable 
to the scope of physics in general; therefore, its adop- 
tion for consistent use in the field of atmospheric elec- 
tricity is recommended. In this system, the interna- 
tional standards for volt, ampere, etc., are employed. 

Auxiliary Equipment and Practical Suggestions 

The atmospheric electrical problems of measurement 
consist predominantly of the measurement of potential 
differences of medium magnitude and of minute elec- 
trostatic charges. They belong, therefore, to the do- 
main of electrometry proper. Although increasing use 
is being made of "vacuum tube electrometers" (d-c 
current amplifiers or d-c voltage amplifiers), thorough 
familiarity with the electrometer is a prerequisite for 
work in atmospheric electricity. 

All electrometers are based on the principle of elec- 
trostatic attraction or repulsion. An exception is the 
capillary electrometer which utilizes the change in the 
sui'face tension of mercury when traversed by an elec- 
tric current. Therefore, strictly speaking, the capillary 
electrometer represents a type of galvanometer [103]. 
Quadrant electrometers have long oscillation periods 
and are therefore suited chiefly for the measurement of 
constant potential differences, whereas filament elec- 
trometers adjust themselves aperiodically and almost 
instantaneously at sensitivities that are not excessively 
high. The highest sensitivities are attained with the 
modern modifications of the quadrant electrometer. 

Figure 1 shows schematically the well-known prin- 
ciple of the quadrant electrometer. Special electrometer 
types are: the model developed by Elster and Geitel 



* Translated from the original German. 



[37], particularly suited to photographic recording; the 
Dolezalek electrometer [30, 31] for high sensitivities; a 
special design by Schultze [119]; the "Binanten" elec- 
trometer [49] and the "Duanten" electrometer of Hoff- 
mann [48, 50, 51]; the Benndorf electrometer [11, 12], 
the familiar, low sensitivity quadrant electrometer for 
mechanical recording of potential gradients. 

Figures 2 and 3 are sectional drawings of the bifilar 
electrometer without auxiliary potential and of the 
unifilar electrometer with auxiliary potential according 
to Wulf's design [152]. More modern designs for attain- 
ing the highest sensitivites include those of Lindemann 
and Keeley [85], Compton [26, 27], Shimizu [127], Swann 
[139] and Perucca [104, 105]. 

The development of the so-called electrometer tubes 
with their characteristically high insulation of the con- 
trol grid and very low grid current (10~^^ amp and less) 
has resulted in the substitution of vacuum-tube elec- 
trometers for the ordinary electrometers. Many types 
of electrometer tubes are now commercially available. 
During continuous operation, maintenance of a con- 
stant zero point is sometimes difficult; some ameliora- 
tion can be provided by using oversized filament bat- 
teries and by the use of selected pairs of tubes in a bridge 
circuit (for further details see, for example, [22, 28, 36, 
46, 47, 69, 77, 82, 106, 109, 114]). 

There are several types of circuits available for use 
with quadrant and filament electrometers provided with 
auxiliary potentials: In the idiostatic circuit the needle 
(lemniscate or electrometer filament) and one pair of 
quadrants (knife edge) are grounded; the unknown 
voltage is applied to the other pair of quadrants (knife 
edge). The deflection is proportional to the square of 
the unkno^^'n voltage, thus making possible a-c meas- 
urement. In the quadrant circuit the needle is at a fixed 
high voltage; one pair of quadrants is grounded, and 
the unknown voltage applied to the other. Deflection 
is proportional to the unknown voltage. The hetero- 
static or needle circuit has both pairs of quadrants con- 
nected to a fixed auxiliary voltage of opposite sign and 
the unknown voltage applied to the needle. This is the 
most frequently used and most sensitive circuit, and 
has the lowest capacitance. In the current circuit the 
voltage measurement is made at the terminals of a re- 
sistor which is usually of the high-ohmic type. 

Measurements of atmospheric electricity are almost 
exclusively electrostatic measurements and therefore 
call for high quality of the dielectric materials. The 
best insulating materials are the natural products, am- 
ber and sulfur. Good substitutes include high quality 
plastic dielectric materials such as hard rubber (ebon- 
ite), plexiglass, and Trolitul. Meticulous surface treat- 



144 



MEASUREMENT OF ATMOSPHERIC ELECTRICITY 



145 



ment is particularly important. Such treatment includes 
high polish, drying, dust removal, paraffin coating in 
some cases, and protection against direct sunlight. 
When working in the open air, careful maintenance of 
the dryness of the dielectric surfaces by drying with 
hot air or by electrical heating is essential. The relative 
humidity on the insulator must not exceed approxi- 




Fig. 1. — Schematic diagram of a quadrant electrometer. 




Fig. 2. — Wulf's bifilar electrometer. 

mately 80 per cent. Figuie 4 gives one example of a 
suitable form of open-air insulator which has held up 
well in practice. 

To combat insects and spiders it is helpful to paint 
the metal parts about the air gap with an adhesive 
substance (fly-paper glue) and also with aromatic insect 
repellants. To eliminate air-borne spider threads in 
summer and fall, mechanical methods must be applied. 

In all electrostatic measurements it is essential to 



maintain good grounding of all parts to be maintained 
at zero potential. In general, grounding to a water pipe 
is satisfactory. It is particularly important that all 
parts to be grounded are connected to the same ground 




Fig. 3. — Wulf's unifilar electrometer. 




,>y<WVx-...\-xV-V:<N 



ff 



M 




3. 



CaClj 



Fig. 4. — Open-air insulator for large mechanical load 
(antennas and the like). 

connection. All othei leads must be protected from 
induction by shielded cables. 

With high electrometer sensitivities undesirable dis- 
turbances may appear as a result of certain unforesee- 
able phenomena in the insulating dielectric material, 
such as the formation of deposits and polarization 
phenomena. Direct creep of charges across an insulator 



146 



ATMOSPHERIC ELECTRICITY 



can be prevented by double insulation separated by a 
grounded metal plate. In all cases, when working with 
maximal sensitivities, it is judicious to protect the in- 
sulators against either direct or indirect influence of 
electric fields by shielding them. 

On many occasions, especially when working with 
movable parts such as rotary collectors, unwelcome 
concomitant phenomena are possible as a result of the 
Volta effect. The latter must be determined and cor- 
rected for by check tests. 

In electrostatic work, the almost universal contam- 
ination of rooms by a-c fields produced by the electric 
light network is a source of serious disturbance. Its 
effect can, in general, be easily recognized and elim- 
inated when working with electrometers. When am- 
plifiers are used such a-c fields may easily lead to errors 
of measurement and misinterpretation (apparent at- 
mospheric electrical potential gradient in rooms) be- 
cause of unintended and undetectable rectifier action. 

Batteries are preferable to rectified a-c lines as sources 
of constant potential, especially in electrometric work. 
Portable high-voltage sources for counting-tube meas- 
urements in open country are described elsewhere 
[133, 136]. 

High ohmic resistors up to about 10'' ohms are fab- 
ricated commercially by evaporation of thin platinum 
films on quartz or amber. For homemade high ohmic 
fluid resistors, radioactive (Bronson) resistors, and other 
possibilities, see von Angerer [3]. 

Ions and Other Atmospheric Suspensions 

Ionizers of the Atmosphere. The ionization of the 
lower atmospheric layers, aside from occasional local 
ionizers of subordinate significance (waterfall effect, 
combustion gases), is caused by the a, /3, and 7 radia- 
tion of radioactive substances and by cosmic radiation. 
The special methods for measuring radioactive sub- 
stances and cosmic radiation are treated elsewhere in 
this Compendium.' 

The ionization in a sealed chamber is due to radia- 
tion from the chamber walls (mathematical determin- 
ation according to von Schweidler [120], experimental 
determination in mines [17]), radiation from the earth, 
radiation from the atmosphere, and cosmic radiation. 
The mathematical estimation of the radiation from the 
earth and the atmosphere is made as follows; 

If Pe.irtii and Pair are the concentrations of radium, or 
of its flaC-equivalent, in a cubic centimeter of earth 
or of air, dearth and /xair the absorption coefficients of 
the corresponding 7-radiation in earth or in air, and if 
K is the "Eve number" (4.0 X 10^ in the absence of 
secondary radiation, approximately 5 to 6 X 10' in 
thick- walled ionization chambers), the ion production 
q (i.e., number of ion pairs formed per cubic centimeter 
per second) is given by 

Radiation instru- (1) 

dearth (0) = 2xpearthif //dearth, meut directly ou thc 

earth's surface 



Radiation instru- (2) 
dearth = 4irpeartiijK^/Mearth, meut iu the ground 

(caves, tunnels, etc.) 

Radiation instru- (3) 
dearth (/i) = gearth(O)0(/iMair), mcut at au altitude 

h above the earth's 
surface 

wherein 



J/»00 — M 
— du, 
X u 



q&h (0) = 27rpairS^/Mair, Radiatiou instru- (4) 

ment on the surface 
of the earth 



ffair = 4TPair^/Ala 



For great altitudes (5) 



Portable radiation devices, which are convenient to 
manipulate, have been described elsewhere [78, 79, 
151], as have counting-tube instruments for field work 
[133, 136]. 

Conductivity, Concentration of Ions, and Ion Mobility. 
If an electric potential is applied to two electrodes in 
an ionized gas, a weak current begins to flow. Corre- 
sponding to the two oppositely flowing ionic currents, 
the current density is the combination of two terms: 



i = e(/cini -|- kin-i)E = AE, 



(6) 



where e is the charge of the ion and equal to 1.6 X 
10"'^ amp sec, E is the field intensity, ni and Ui denote 
the number of positive and negative ions, and fci and 
/c2 represent the mobility of the positive and negative 
ions, respectively. The expression e(kini -f k^ni) = A 
is designated as the (total) conductivity of the gas. 
The terms 

Xi = fcinie and X2 = kiriit 

are the positive and negative polar conductivities of 
the ionic conductor. 



4- 



POTENTIAL 



IE 



TSL 



1. Consult "Radioactivity in the Atmosphere" by H. Israel, 
pp. 155-161. 



I n 

Fig. 5. — Schematic curve of the current-potential relationship 
(characteristic) in an ionized gas at rest. 

If the voltage is increased starting from zero, a 
gradual decrease in ion content results; the current 
does not rise in proportion to the voltage and remains 
constant after a given value of voltage has been at- 
tained. Accordingly a distinction is made between ohmic 

2. For a tabulation of this function, see [86]. 



MEASUREMENT OF ATMOSPHERIC ELECTRICITY 



147 



current (I), semi-saturation current (II), and saturation 
current (III); see Fig. 5. 

To attain clearer experimental conditions, it is now 
a general practice to employ the aspiration condenser 
in connection with the so-called method of perpendicular 
velocities as follows: When air containing ions flows 
through a condenser to which an electric field has 
been applied, the trajectory of an ion is found to be 
the resultant of the two mutually perpendicular forces, 
namely, that of the air current and that of the field. 
If M is the aspirated quantity of air in cubic centi- 
meters per second, C is the condenser capacitance (C = 
L/[2 In (R/r)] for cylindrical condensers having radii 
R and r and length L), and V is the potential in volts, 
the expression 



k, = M/iTCV 



(7) 



represents the limiting mobility of the condenser and 
states that all ions whose mobility is greater than, or 




(q) 




Fig. 6. — Schematic diagram of the current-potential char- 
acteristic in the aspiration condenser (a) in the presence of 
one type of ion, (6) in the presence of several types of ions. 

at least equal to, this mobility are deposited. Of those 
ions, whose mobility k is smaller, only the percentage 
k/kg is deposited. 

It is evident that, in the foregoing, the characteristic 
relationship between current and potential in the con- 
denser will be a broken linear curve. This curve will 
resemble Fig. 6a when but one type of ion is present, 
and assume the form of Fig. Gb when several types of 
ions occur. From the preceding statement, the following 
conditions are found for the measurement of ions: 

Conductivity: M must be chosen so great or V so 
small that operations take place in the first segment 
of the curve that rises from the origin of the coordinate 
system. 

Ion Counts: Determined from the saturation current. 

Ion Mobility: Each break in the curve yields, accord- 
ing to equation (7), the mobility of a corresponding 
type of ion. 



Ion Spectrum (numerical distribution on the basis 
of the individual mobilities) : The number pertaining 
to a given mobility results from the magnitude of the 
change in slope of the characteristic; expressed in terms 
of differentials, the ion spectrum is determined by the 
second differential quotient of the characteristic. 

Additional methodological details are given else- 
where [54, 56, 57]. With respect to "edge disturbances" 
(effect of the inhomogeneity of the field at the edge of 
the condenser), see Itiwa,ra [73], Israel [56], and others. 
For special designs, that homogenize the field of cylin- 
drical condensers, refer to Becker [8], Swann [137], and 
Scholz [115]. 

Well-known instruments that are easy to manipulate 
include the Gerdien aspirator [39, 40] for measurements 
of conductivity; the Ebert ion counter [32, 33, 35] and 
the Weger aspirator [58, 142] for measurements of the 
concentration and mobility of small ions (see references 
[6, 41, 42, 142] for errors of the Ebert instrument), and 
the Israel ion counter [55] for counts of medium and 
larger ions. 

Mobility measurements by means of divided con- 
densers are described in the literature [18; 19; 29; 54, 
pp. 179 ff.]; a differential method of very great resolving 
power had been proposed by Benndorf (e.g., see [54, 
56, 57]). Recording devices for conductivity measure- 
ments are also described in the literature [82, 108, 115, 
116, 138]; recording instruments for counting ions have 
been devised by Nordmann [94-96], Leckie [82], Lange- 
vin [81], Hogg [52, 53], and others. 

Schering's method [110, 111] for recording conduc- 
tivity, which is still used occasionally, is somewhat 
different. A wire from 10 to 20 m long is freely sus- 
pended and surrounded by a cylindrical wire net having 
a radius of approximately 1 m. The wire is charged at 
certain time intervals and its voltage drop is recorded, 
for instance, by a Benndorf electrometer. 

Rates of Ion Formation and Recombination; Mean 
Life of Ions. Under conditions of equilibrium, the rate 
of ion production q and the numbers n, N, and A'o of 
the small ions, large ions, and uncharged suspensions, 
respectively, have the following relationship: 

q = an'^ + vinN + TjjniVo + m^No + mN- (8) 

where 

a = recombination coefficient between small ions, 

r;i = recombination coefficient between small and 
large ions, 

rj2 = recombination coefficient between small ions 
and uncharged particles, 

7^3 = recombination coefficient between large ions 
and uncharged particles, 

Tji = recombination coefficient between large ions. 
The last two terms of equation (8) are insignificant as 
compared to the others, because vs and 7/4 are smaller 
than the other coefficients by several orders of magni- 
tude. 

In order to determine the individual recombination 
coefficients, synchronous measurements of all partici- 
pating constituents are necessary [92, 93]. Owing to 
the prerequisite of ionization equilibrium, .such meas- 



148 



ATMOSPHERIC ELECTRICITY 



urements are very difficult [60, 63]. However, according 
to von Schweidler [121-123], the following visualizable 
approximation can be made: Under natural conditions 
near the ground where moderate to high values of iV 
and A'o prevail, we can write instead of equation (8) 



= an''- + /3ft = /3'n, 



(9) 



since the quadratic term becomes less important in 
comparison to the linear one, as the concentration of 
large ions in the air becomes greater. The coefficient 
/3', which has the unit of sec~^, is designated as the 
vanishing constant. Its reciprocal then is the mean life 
of small ions, in analogy to radioactive phenomena. 

In practice, the air is introduced into an ionization 
chamber (condenser, sealed on all sides). By applying 
a high voltage, tlae value of n present is determined, 
and then the characteristic current-potential relation- 
ship is recorded. The values for q and n are determined 
by means of Method I (ohmic current), or q and /3 are 
found by Method II (semisaturation current) ; for more 
details, see the references previously cited. 

Condensation Nuclei and Dust Particles. Aside from 
the hydrometeors (fog, clouds, and precipitation), the 
atmospheric content of suspended particles is some- 
what arbitrarily divided into condensation nuclei and 
dust particles. Condensation nuclei, hygroscopic par- 
ticles whose i-adius is approximately 10~^ cm or less, 
are counted by producing condensation upon them in 
supersaturated air and determining the number of re- 
sulting droplets. Two types of such nuclei counters are 
well knottTi. One was developed by Aitken [1] and the 
other by Scholz [117, 118]. For details, see these papers 
as well as others [23, 71, 80]. 

The measurement of dust particles is made bj^ means 
of the Owens counter [9] and the Konimeter.^ 

The Electric Field of the Atmosphere 

If an uncharged conductor of any given shape is 
introduced into the earth's field, a separation of electric 
charges is found on this conductor, due to electrostatic 
induction. The conductor assumes the potential Vl, 
which is the potential of a given equipotential layer in 
the earth's field. This layer intersects orthogonally the 
electrically neutral line nn of the conductor's surface. 
It is the potential of the reference point B (see Fig. 7). 
The following possibilities exist for measurements of 
the electric field. 

1. The body is temporarily grounded in the position 
shown in Fig. 7. Under such conditions it assumes the 
zero potential of the earth and takes on a charge Q — 
—CVl (where C = capacitance) from Avhich, when it 
is introduced into a field-free space ("shielding"), the 
difference in potential of Vl with respect to the ground 
can be determined (electrostatic induction method). 
Variations of the method illustrated in Fig. 7 include: 

a. The body is grounded, then insulated, and trans- 
ferred to another point in the field. In this way its 
electrostatic induction is changed. Measurement of this 
"free induction charge" furnishes a measure of the dif- 

3. Described in the Zeiss catalogue, Jena. 



ference in potential of the reference points of both posi- 
tions. (For the principle of the movable conductor see 
[2; 7; 108; 137, p. 182]). 

b. If after temporary grounding the body remains 
in position, its changes in electrostatic induction give 
a measure of the variation of the field; by means of 
high-ohmic leaks, the arrangement is converted into a 
field variometer [59]. 

c. If a metal plate is mounted flush with the earth's 
surface, grounded and exposed to the field, and there- 
upon shielded against the latter in an insulated state, 
it furnishes the surface density of the electrostatic in- 
ductance charge and thus the field intensity at the 
ground level (Wilson test-plate [146-149]). Rhythmical 
exposure to and shielding from the field produces an 
a-c current [87, 89-91, 124]. 

2. If provisions are made for the removal of the 
induction charge at a point P not situated on the neu- 
tral line of the conductor, a new neutral line is pro- 
duced to which a different equipotential surface Vu 




Fig. 7. — Electric field conditions produced by an uncharged 
conductor. 

orthogonally connects (see Fig. 8). A connected meas- 
uring instrument indicates the potential of the reference 
point R with respect to the ground. Discharge of the 
electrostatic induction is attained by so-called collectors 
as enumerated herewith: 

a. Point collector, based on the point discharge flow 
(no longer in use). 

b. Flame collector, utilizing the ionization of the 
gases of combustion to conduct the charge away; a 
variant is the glow collector. 

c. Water-dropper collector, operating by capacitive 
charge separation and discharge. 

d. Radioactive collector, which provides for discharge 
by ionization of its environment. 

The discharge proceeds according to an exponential 
law: 



Ut = Uoe- 



KlIC 



(10) 



where Ut is the potential difference at the time t, Uo 
the potential difference at the time zero, C the capaci- 
tance, and K the discharge constant. The discharge con- 
stant K or its reciprocal, the "apparent" or "transition" 



MEASUREMENT OF ATMOSPHERIC ELECTRICITY 



149 



resistance, serves as an index of the efficiency of a col- 
lector. The value of k fluctuates from approximately 




Fig. 8. — Electric field conditions produced by a collector. 

unity for glow collectors to 50-100 X lO"'- for highly 
radioactive collectors. 

The "external resistance," in other words, the resis- 
tance of the insulation of the collector from the ground, 
must be great compared to the transition resistance of 
the collector, as otherwise its readings become inaccu- 
rate. Attempts to operate the collector "short-circuited" 
were found to be subject to disturbances, for example, 
by the wind, and should therefore be avoided [77]. 

Exact field measurements can only be performed by 
means of the Wilson test-plate on completely level 
terrain. Any other type of arrangement disturbs the 
field and yields only more or less acceptable approxi- 
mations. The so-called technique of reduction to the 
free plane can only be used as an approximation [16]. 
For this reason a comparison of "absolute values" of 
the field will always remain somewhat problematical. 
Therefore, consideration of the relative periodic and 
aperiodic variabilities of the electric field is funda- 
mentally more important. 

With respect to the selection of "undisturbed days" 
in the treatment of recorded data, see, among other 
sources, Israel and Lahmeyer [72]. 

The Vertical Current 

The difficulties involved in measuring and recording 
the vertical electric current stem from the generally 
minute current density of about 10"'^ amp m~^ and the 
disturbing effects of the electrostatic inductance of the 
field or of its changes on the receiver system. Galvano- 
metric methods are applicable only to measurements of 
vertical currents intensified by thunderstorms. There- 
fore, accumulation methods (accumulation of inflow of 
charges over a given time) ai'e used in most cases 
(Ebert [34], Simpson [128], and Wilson [146-149]). The 
disadvantage of these methods is that in the accumu- 
lation period the potential of the collecting body changes 
somewhat. Simpson circumvents this disadvantage by 
continuous draining of the charges by means of a water- 
dropper collector, whereas Wilson obviates the diffi- 
culty by a compensation method (see Fig. 9). Methods 



for continuous recording are described by Scrase [125] 
(accumulation method, quadrant electrometer) as 
shown in Fig. 10, and by Kasemir [77] (direct recording 
by use of a d-c amplifier). Scrase compensates for the 
effects of field fluctuation by using a supplementary 
field collector connected to alternate quadrants in the 
quadrant electrometer, whereas Kasemir largely sup- 




ELM. 



Fig. 9. — Diagram of the Wilson test-plate method (K is a 
variable condenser and ELM is the electrometer). 




Fig. 10. Schematic diagram of the vertical -current recorder 
after Scrase (B is the radioactive collector, P is the test plate, 
and ELM is the quadrant electrometer). 

presses these effects by increasing the capacitance. The 
vertical current can also be computed from the poten- 
tial gradient and the conductivity, according to equa- 
tion (6). 

The Space Charge 

Measurement or recording of the space charge is 
made by means of the following methods: The cage 
method consisting of the measurement of the potential 
difference between the wall siu-face and the center of 
a wire cage whose volume ranges from approximately 
one to several cubic meters [75, 76] ; the method of the 
change of the potential gradient with altitude according 
to Poisson's equation [13, 97, 145]; Obolenski's filter 
method [102]; or the method of synchronous counts of 
positive and negative ions [53, 82]. The cage method is 
disturbed in most cases by Volta effects [15]. 



150 



ATMOSPHERIC ELECTRICITY 



Investigations of Thunderstorm Electricity 

Field. Measurements of atmospheric electricity in 
conjunction with electrical storms require a very rapid 
response of the equipment. This requirement elim- 
inates collector measurements. The measurements are 
based on the application of electrostatic induction tech- 
niques of field measurement (Wilson test-plate, Wilson 
elevated sphere, mechanical collectors, antennas) in 
combination with high-speed recording instruments in- 
cluding cathode-ray oscillographs. 

Current. The vertical current can be determined with 
the aid of the Wilson test-plate in connection with a 
galvanometer or a capillary electrometer [148] or by 
recording the current through a point collector mounted 
in an exposed position [143, 150]. 

Precipitation Charge. Precipitation is collected in an 
insulated vessel. Splashing of the drops is prevented by 
lining the bottom with velvet, brushes, etc. Records 
are obtained either by the accumulation technique or 
by the "current-circuit method." For charge measure- 
ments on individual drops see Chalmers and Pasquill 
[25], Gschwend [43], and Gunn [44]. 

Investigations of Lightning Discharges.'^ The following 
methods can be employed: The optical method involves 
photography, using, for example, the Boys camera [20, 
21]. 

In the electrical method the Klydonograph is used 
for the direct measurement of peak voltages in the 
lightning discharge by means of Lichtenberg figures; 
the measuring range is approximately 2-18 kv [83]. 

The magnetic method is based on the magnetization 
of small steel rods by currents flowing through light- 
ning rods of various types [38] as, for example, the 
Fulchronograph [140, 141], or on the measurement of 
the magnetic field of the lightning discharge channel, 
and on numerous other special methods some of which 
are used in combination with high-tension lines [84, 
99, 100, 144]. 

Radio Interferences. The electromagnetic pulses (at- 
mospheric) originating from electric discharges in the 
atmosphere are investigated with respect to their num- 
ber, direction of incidence, place of origin, and pattern. 
Excitation of an oscillating circuit coupled to a non- 
directional antenna gives the number; use of rotating 
loop antennas gives the directional distribution ; ranging 
with cathode-ray direction finders furnishes a bearing 
on the point of origin; finally, the pattern of the dis- 
turbance is established by use of aperiodic d-c ampli- 
fiers. For literature of the foregoing see: Appleton and 
collaborators [4, 5], Bureau [24], Lugeon [88], Norinder 
[98, 101], Schindelhauer [112, 113], and numerous others. 

Measurements in the Free Atmosphere 

The methods used for determination of the individual 
factors of electricity in the free atmosphere are funda- 
mentally the same as those used at ground level. They 
must, however, be properly modified to allow for the 
special operational conditions obtaining in either the 

4. Consult "The Lightning Discharge" by J. H. Hagenguth, 
pp. 136-143 in this Compendium. 



free-flying or captive carriers of the measuring instru- 
ments, such as manned free balloons, gliders, motor- 
driven aircraft, dirigibles and blimps, automatic re- 
cording balloons, captive balloons, and kites. For a 
summary of older and more recent aerological methods 
of atmospheric electricity see Israel [65]. 

Problems of Present-Day Research in Atmospheric 
Electricity 

In concluding this discussion of equipment and 
methods, a few ideas may be presented on the most 
urgent problems of modern research in atmosphei'ic 
electricity. 

Although measurements have been made for almost 
two hundred years, the phenomena of atmospheric 
electricity have been considered a discrete part of the 
physics of the atmosphere; it is only recently that cer- 
tain fundamental relationships to other atmospheric 
phenomena have been uncovered. Through the gradual 
detection of the inner relationships between atmos- 
pheric-electric and meteorological processes, new light 
is being shed on many of the electric phenomena that 
hitherto have been unexplained. Moreover, the possi- J 
bility arises of immediate application of the knowledge * 
gained in atmospheric electricity to meteorology and 
aerology. 

As has recently been pointed out [68], the funda- 
mental concepts of atmospheric-electric phenomena 
have undergone a mutation in that the tendency for 
segregation of electric from meteorological processes is 
slowly disappearing and is giving way to a trend toward 
correlating them. The stimulus for this development 
has been primarily the knowledge gained through the 
ocean expeditions sponsored by the Carnegie Institu- 
tion. These cruises have revealed the world-wide syn- 
chronous component of the electric field, the coupling 
of this field with the world-wide weather, and the in- 
creasingly clear relationships between the local varia- 
tions and the vertical mass exchange. 

This last correlation, in particular, may furnish the 
key to the major portion of the relationship between 
atmospheric-electric and meteorological phenomena and, 
thus, simultaneously indicate the direction in which 
further research should proceed. 

A primary requirement is the extension of the meas- 
urements to more than a single atmospheric-electric 
element, because the prevalent practice of recording the 
potential gradient alone permits only very limited con- 
clusions. The three fundamental quantities of field in- 
tensity (potential gradient) E, conductivity A, and ver- 
tical current density i, are interrelated in Ohm's law: 

EK = i. 

Any statements regarding processes taking place in the 
atmospheric-electric circuit under equilibrium condi- 
tions require that two of these fundamental quantities 
be known. If we are to include the nonstationary 
("switching-on") processes, all three quantities must 
be measured. It would be most desirable if this prac- 
tice, now followed by the large atmospheric-electric 



MEASUREMENT OF ATMOSPHERIC ELECTRICITY 



151 



observatories, were introduced everywhere. (For de- 
tails see [62, 72].) 

For investigations of the effect of aiistausch on at- 
mospheric-electric conditions, a simplified case must 
first be attacked by means of recordings made at alti- 
tudes as high as possible. Such investigations, con- 
ducted at high mountain observatories, promise free- 
dom from changes in the aerosol that, in the lower 
atmospheric layers, are the result of the diurnal varia- 
tion of the vertical mass exchange. We may expect that 
the atmospheric-electric processes in their entirety are 
composed of the interaction of low-level phenomena, 
which proceed according to local time and are caused 
by austausch variations, and of the world-wide syn- 
chronous processes at higher levels. We may also expect 
the transition to occur at an altitude of a few kilometers 
[61, 68]. For preliminary results of pertinent investiga- 
tions see [70]. 

The following experiment appears to be an additional 
promising step in this dii'ection. A program could be 
set up to obtain simultaneous records of atmospheric- 
electric elements at neighboring stations located at dif- 
ferent altitudes. This would offer the possibility of 
observing the gradual upward penetration of the aus- 
tausch effect [67]. 

In this connection, further investigation of the diur- 
nal variations of atmospheric-electric elements in vari- 
ous air masses [64, 66] can be expected to furnish 
criteria of the degree of stability or instability of at- 
mospheric stratification. 

Research in the vicinity of "generators," that is, in 
the region of thunderstorms, precipitation, and clouds, 
offers special problems; see, for example, the work by 
Simpson [129, 130]. 

Without doubt, the greatest problem of atmospheric 
electricity is its systematic extension into the third 
dimension, that is, the development of an atmospheric- 
electric aerology with regular determinations of the 
conditions existing in the free atmosphere [65]. Recent 
developments of special methods of measurement suit- 
able for this purpose, such as those by Simpson [131, 
132], Rossmann [107], Gunn [44, 45], and Belin [10], 
furnish the practical means for this extension. 

The exploration of the origin and propagation of 
high-frequency disturbances in the atmosphere (sferics) 
can materially aid weather reconnaissance and analysis 
[4, 5, 88, 113] and can be developed into an integrating 
component of meteorological practice. 

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154 



ATMOSPHERIC ELECTRICITY 



120. ScHWEiDLER, E. V., "IJber die lonisierung in einem 

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(1914). 



RADIOACTIVITY OF THE ATMOSPHERE* 

By H. ISRAEL 
Buchau Observatory and University of Tubingen 



Introduction 

The conductivity of the air is a characteristic of the 
entire atmosphere at all times. It is the result of the 
most varied ionizing radiation of a corpuscular and 
electromagnetic nature. In the lower layers of the at- 
mosphere the radiation of the radioactive substances 
that are contained in the air and in the uppermost 
strata of the earth's crust is the principal source of this 
ion formation. 

Table I gives a summary of the three decay series of 
radioactive substances and the physical qualities of the 
respective types of atoms. As far as the atmosphere is 
concerned, our interest begins only with the gaseous 
intermediate transformation products {i.e., the emana- 



The discovery of radioactive substances in the atmos- 
phere was made by Elster and Geitel [19], who thus 
gave a physical explanation for the weak conductivity 
of the air, already known to Coulomb in 1785. 

Methods of Measurement 

There are two possible methods of measuring the 
radioactive elements of the atmosphere. One method 
consists of removing the emanations from the air by 
adsorption or condensation and measuring them in an 
ionization chamber (emanometry). In the second 
method, the property of so-called "inductions" is uti- 
lized, that is, the property of some radioactive decay 
products of carrying a positive electrical charge; these 



Table I. Radioactive Substances in" the Atmosphere 



Element 



Radon 

Radium A. . 
Radium B. . 
Radium C . . 
Radium D.. 
Radium E. . 
Radium F* , 

Thoron 

Thorium A . 
Thorium B . 
Thorium C . 
Actinon .... 
Actinium A. 
Actinium B. 
Actinium C. 



Symbol 



Rn 

BaA 

RaB 

RaC 

RaD 

RaE 

RaF 

Tn 

ThA 

ThB 

ThC 

An 

AcA 

AcB 

AcC 



Rays 



/3 + T 

/3 + 7 

(3 -1-7 

«(+^)t 



a + 



+ 7 
(3-1-7 



+ y 

f /3 + 7 



Half-life 


Disintegration constant 
(sec-') 


3.825 day 


2.097 X 10-= 


3.05 min 


3.78 


X 10-3 


26.8 min 


4.31 


X 10-^ 


19.7 min 


5.86 


X 10-* 


22 yr 


1.00 


X io-» 


5.0 day 


1.61 


X 10-6 


140 day 


5.73 


X 10-8 


54.5 sec 


1.71 


X 10-2 


0.14 sec 


4.95 




10.6 hr 


1.82 


X 10-5 


60.5 min 


1.91 


X 10-^ 


3.92 sec 


0.177 




2 X 10-' sec 


347 




36.0 min 


3.21 


X 10-^ 


2.16 min 


5.35 


X 10^' J 



* Polonium (Po) f uncertain 

tions) and therefore a consideration of all preceding 
elements has been omitted. 

The gaseous emanations radon (Rn), thoron (Tn), 
and actinon (An) are emitted from the rocks and the 
soil into the air entrapped in the ground capillaries or 
directly into the air at the earth's surface and are 
transported to higher levels by the apparent diffusion 
of the vertical atmospheric mass exchange (austausch). 
Because of the interaction between this exchange and 
the disintegration rate of the emanations and their by- 
products, a certain characteristic vertical distribution 
for each element can be expected which, in the mean, 
can be proven experimentally (see below). The contri- 
bution made by these radioactive elements to the for- 
mation of ions in the atmosphere decreases rapidly with 
altitude and ceases approximately at the height of the 
tropopause. 



■ Translated from the original German. 



products are deposited on negatively charged collectors 
where their ionizing effect can be examined. This tech- 
nique is termed the "induction method." The experi- 
mental technique of the induction method is simpler 
than that of emanometry, but quantitatively less relia- 
ble. Therefore, emanometry is to be preferred for analy- 
sis of the relatively long-lived Rn. However, direct 
emanometry does not work for Th- and 4c-products 
because of the short life of Tn and A71, and only the 
indirect induction method is possible. 

Emanometry. The international unit of Rn is the 
mric (C). The curie is the quantity of radon which is 
in radioactive equilibrium with one gram of radiimi 
and thus emits as many alpha particles per unit time 
as does one gram of radiiun. The current which 1 C 
can maintain at saturation and with complete utiliza- 
tion of its radiation is 9.22 X 10-* amp. In the course 
of approximately 3 hr, equilibriiun is reached between 




155 



156 



ATMOSPHERIC ELECTRICITY 



Rn and its three short-lived decay products, RaA, 
RaB, and RaC. The current is thereby increased to 
20.0 X 10"'* amp.' These two "current equivalents" are 
the basis for emanometry. 

A closed cylindrical vessel containing an insulated 
electrode is generally used as an ionization chamber. 
Between the walls of the vessel and the electrode, a 
potential of a few hundred volts is applied which causes 
the ions produced to deposit before their number 
changes appreciably by recombination (saturation cur- 
rent). As the ion concentration in the air is small, the 
measurement is usually made electrometrically by the 
charge or discharge method shown in Fig. 1. 



1 E 
I 



TmriTi. 



7mm. 



(q) (b) 

Fig. 1. — Circuit diagram for emanometrical measurements 
by the charge method (a) and by the discharge method (6). 

Conversion of the measured data into radon units 
requires various corrections: 

1. The "time correction" considers the change of 
the current equivalent due to formation of RaA, RaB, 
and RaC. Formerly, measurements were not begun 
until radioactive equilibrium had been attained be- 
tween Rn and RaA, RaB, and RaC, at the earliest 
about 3 hr after pure Rn had been put into the measur- 
ing vessel. This method can now be shortened by using 
the intermediate values of the current equivalent 
(Table II). 

2. Because of the limitation of the ionization space, 
not all alpha rays can become fully effective. Great 
difficulties are encountered in the numerical computa- 
tion of the correction factor [14, 21, 54]. Therefore, the 
following empirical corrections developed by Duane 
and Laborde [16, 17] are used in most cases: 

J = K (1 - 0.517 0/V) 
J' = K' a- 0.572 0/V), 

where J and J' represent the measured current values 

1. In this case onlj^ 50 per cent of the ionization effect of the 
alpha rays from RaA, RaB, and RaC is considered, since these 
inductions deposit on the walls. The beta and gamma radia- 
tions from RaB and RaC constitute less than 1 per cent of the 
current and are usually not considered. Furthermore, the con- 
tribution of RaD, RaE, and RaF is far below the range of 
accuracy of measurement and may be disregarded. The only 
manifestation of these substances is the slowly increasing 
"pollution" of the measuring chamber which can usually be 
eliminated mechanically. 



for pure Rn or for radon in equilibrimn with RaA, 
RaB, and RaC; K and K' are the corrected current 
values; is the surface, and F the volume of the ioni- 
zation vessel. 

3. It is difficult to attain saturation in ionization by 
alpha radiation, because a very strong initial recombi- 
nation becomes effective in the closely packed ion 
columns concomitant to their formation. In this case, 
also, theoretical determination of a satisfactory correc- 
tion factor is impossible. A generally valid empirical 
correction cannot be found either, since the saturation 
deficit is a function of the shape and size of the vessel 
and of the total quantity of ionizing substances. There- 
fore, this correction must be determined individually 
for each type of emanometer for varying quantities of 
radon. Suggestions for its practical evaluation have 
been made by Israel [31]. 

4. The effect of the atmospheric pressure and tem- 
perature on emanometrical measurements can be con- 
sidered according to Lester [36]. In general, however, 
it remains a minor error compared with the other errors 
present [6]. 



Table II. 



Current Equivalents St for Emanometrical 
Measurements* 



t 


St 


/ 


(min) 


C10-« amp) 


(min) 





9.22 


60 


2 


11.03 


80 


4 


12.21 


100 


6 


12.97 


150 


8 


13.48 


200 


10 


13.80 


250 


?0 


14.69 


300 


30 


15.34 


400 


40 


16.00 


500 



St 
(lO-i amp) 



17.25 
18.24 
18.91 
19.78 
19.98 
20.00 
19.95 
19.80 
19.61 



* Values of St are for t minutes after the introduction of 
pure Rn into an ionization chamber, taking into account the 
disintegration of Rn. 

These corrections may be avoided if the measure- 
ments are compared with those of known quantities of 
radon. In order to obtain such small, but well-defined 
Rn quantities, the so-called radium standards are used, 
aqueous solutions of RaCh which can be produced 
easily [8] or which can be obtained commercially. The 
precautions to be taken when working with such test 
solutions are discussed elsewhere [8, 29]. 

Various types of emanometers, especially useful for 
atmospheric Rn measurements, have been developed, 
for example, by Becker [7], Messerschmidt [42, 43], 
Janitzky [33], and Israel [28, 31]. Moreover, such de- 
vices for measurements in an air stream were devel- 
oped by Israel [32] and Deij (see [16, 17]). Since the 
Rn concentration in the air is extremely small, a method 
of enriching it is often used to increase the accuracy. 
This method utilizes the very great solubility of Rn in 
some organic substances, its ability to condense at the 
temperature of liquid air, or, most conveniently, its 
property of being adsorbed by coconut-shell charcoal 
or activated carbon. By heating the adsorbent to in- 
candescence, the Rn will again be given off completely. 
When large ionization chambers are used at high sensi- 
tivity, the "enrichment method" need not be used 



RADIOACTIVITY OF THE ATMOSPHERE 



157 



(lower limit of measurement approximately 2 X 10"" 
C cm~^). For further details see Israel [29]. 

Induction Mdhod. If a charged body is exposed to 
air containing Rn, its surface acquires a certain activ- 
itj', A\'hich becomes greatest with a negative charge. Be- 
cause of this, it is apparent that the resultant products, 
principally RaA, must be positively charged. Accord- 
ing to Eckmann [18], the RaA atoms are in fact posi- 
tively charged immediatelj^ after their formation. 
Hence, they would be useful for an indirect quantita- 
tive Rn measurement, if thej^ did not soon lose part of 
their charge by interaction with the ions in the atmos- 
phere. Furthermore, the other by-products also carry, 
at least in part, electric charges. Finally, it must be 
considered that these charged inductions move under 
the influence of the electric field of the atmosphere. 

All these possibilities of error greatly reduce the re- 
liability of the indirect method of measurement. This 
method supplies only relative values which, when ob- 
tained under similar working conditions, are more or 
less comparable with one another. However, the rela- 
tive values can be correlated with the direct-emission 
measurements only with very great uncertainty. Even 
the various attempts at applying corrections, made by 
Salpeter [49] and Curie [13] did not succeed in elimi- 
nating this uncertainty. Only Eve's and Aliverti's mod- 
ification of the procedure (see below) leads to reliable 
quantitative results. 

The oldest type of a practical technique for carrying 
out such measurements is that in which a wire is kept 
at a high negative potential, exposed for sevei-al hours, 
and then wound on a spool and examined in an ioniza- 
tion chamber. The resultant rate of discharge, expressed 
in volts per hour divided by the length of the wire 
(in meters), is known as the "activation number." An 
extensive improvement of this technique has been in- 
troduced by Swann [56], who segregated the contribu- 
tions of various tj^pes of inductions by observing the 
decrease in wire activity with time. Gerdien [22] and 
Bauer and Swann [4, 5] use an aspiration process for 
collection. Eve [20] exposes the collecting wire in a 
large closed vessel, 16 m^ in volume, and compares the 
resultant activity with that obtained under otherwise 
identical conditions, but with a known quantity of 
Rn in the vessel. In Aliverti's method [1, 2], all induc- 
tions contained in the atmosphere are deposited in a 
manner similar to that of electrostatic precipitators. 
The quantitative values for Rn and Tn can be obtained 
from the discharge curves. 

Results 

From the foregoing discussion, it is apparent that 
the activation numbers can give only an approximate 
picture of actual conditions. The values given in Table 
III represent averages derived from a large number of 
individual tests. 

If we disregard the uncertainties involved, it is ap- 
parent from the values given in Table III that the 
lowest values are found over the oceans, increasing 
toward the shore, and the highest values in high moun- 
tains with strongly emanating igneous rocks. They 



give clear evidence that the radioactive admixtures 
get into the atmosphere exclusively from the conti- 
nents. 

The right-hand column of Table III gives mean 
values of the Rn content after improved induction 
measurements (aspiration method); they probably are 
much too small, particularly over the continents. 

Table III. Average Values Resulting from 
Measurements of Inductions 



Location 


Activation 
number 


Rn content after 

induction measurement 

(C cm.-' X 10-'») 


Oceans 


approx. 10 
approx. 40 

approx. 100 
450-500 


1.9 


Continents 


35 


High Mountains 

Alps 

High Cordilleras 





Direct Rn measurements from various parts of the 
world are available in large number; a summary of 
such measurements is presented in Table IV. It will 
be seen from Table IV that the mean Rn content of the 
atmosphere near the surface over continents amounts 
to about 100-120 X 10"'^ C cm"^ (omitting the larger 
values for the high mountains (Innsbruck) and the 
smaller ones for high altitudes), and over oceans to 
about 1-2 X 10~'^ C cm~^ According!}', one liter of 
air over the continent contains about 2000 atoms of Rn, 
over the oceans about 30 atoms. Thus, there can no 
longer be any doubt that the atmospheric Rn content 
is of purely continental origin; Bongards' assumption 
[12] that the atmospheric Rn is of cosmic origin can 
therefore be discarded. The same conclusion follows 
from the decrease of the Rn content with height (see 
below). 

As far as the Th- and ^4c-products of the atmosphere 
are concerned, data are more scarce. On the whole, it 
can be stated that (1) even over the continents, Tn, 
together with its disintegration products, contributes 
to the entire ionization probably less than, or at best 
just as much as, Rn with its inductions [44], and (2) 
An with its derivatives contributes hardly more than 
3 per cent towards the formation of atmospheric ions. 

The exhalation of Rn {Rn emission of the ground), 
according to the results obtained so far, is of the order 
of approximately 40 X lO"'* C cm-^ sec"' (Table V). 

The exhalation seems to have a single diurnal period 
with a maximum in the early forenoon [39], but its 
variation is strongly modified by meteorological factors 
[35, 61, 63]. The seasonal variation has a maximum in 
late summer [61]. Precipitation reduces the exhalation 
considerably, and solar radiation and an increase in 
temperature raise it; falling atmospheric pressure causes 
an increase of exhalation, rising pressure a decrease. 
Frost decreases it very sharply [63] and can stop it 
entirely [11]. 

Variations of the Atmospheric Radon Content. Over 
flat country and valleys the diurnal curves show un- 
equivocally a single period with a maximum during 
the night (toward morning) and a minimum during 
the afternoon [9, 39]. In mountainous country the 



158 



ATMOSPHERIC ELECTRICITY 



diurnal curves are much less pronounced and apparently 
decisively influenced by austausch phenomena [47], 
inasmuch as for mountain stations well-developed regu- 
lar diurnal variations appear only when there is a strong 
convective exchange of air with lower layers. 

The seasonal variation seems to run parallel to the 
temperature curve, as is shown by the increase of the 

Table IV. Mbasuebments of the Radon Content 
OP THE Atmosphere 



Place and time of meas- 


Author 


Num- 
ber of 


Mean 


Maxi- 
mum 


Mini- 
mum 


urement 




tests 
41 


(Ccm 


-' X 10- 


18) 


Montreal 1907-8 


Eve [20] 


60 


127 


18 


Cambridge 1908-10 


Satterly [50] 


87 


108 


350 


35 


Chicago 1908 


Ashman [3] 


6 


95 


200 


45 


Manila 1912-14 


Wright and 
Smith [60] 


50 


71 


154 


14 


Mount Pauai 1913 


Wright and 


10 


19 


34 


8 


(2460 m msl) 


Smith [60] 










Freiburg, Switzer- 


Olujic [45] 


36 


131 


305 


54 


land 1917 












Innsbruck 1912-20 


Schweidler [53] 


339 


340 


1220 





Seeham-Salzburg 


Schweidler [53] 


207 


114 


405 





1914-18 












Innsbruck 1919 


Zlatarovio [62] 


49 


433 


1140 


40 


Halle 1923-24 


Wigand and 
Wenk [59 




— 


500 


300 


Halle 1923-24 (0- 


Wigand and 


5 


170 


— 


— 


1000 m msl) 


Wenk [591 










(1000-2000 m msl) 


Wigand and 
Wenk [59] 


3 


85 


— 


— 


(>2000 mmsl) 


Wigand and 
Wenk 59] 


3 


8 


— 


— 


Novaya Zemlya 1927 


Bghounek [10] 


— 


1* 


— 


— 


Graz 1928 


Kosmath [34] 


63 


142 


270 


43 


Halle 1931 


Messerschmidt 
[43] 


704 


300 


900 


140 


Turin 1932 


Aliverti [1] 


26 


414 


— 


— 


Innsbruck 1933 


Illing [26] 


201 


436 


2580 


25 


Patscherkofel near 


Israel [39] 


9 


103 


610 


30 


Innsbruck 1933 












(1980 m msl) 












Leiden, Holland 












Land breeze 


Israel 30 


— 


85 


— 


— 


Sea breeze 


Israel 30 


— 


21 


— 


— 


Frankfurt am Main 


Becker [9] 


80 


154 


526 


28 


1933-34 












Taunus Observa- 


Becker [9] 


48 


125 


477 


14 


tory 1933 












Innsbruck 1934 


Macek [38] 


29 


432 


1780 


72 


Bad Nauheim 1935 


Schwalb [52] 


90 


585 


9200 





Innsbruck 1935 


Priebsch, Rad- 
inger and 
Dymek [47] 


225 


312 


1560 


10 


Hafelekar near 


Priebsch, Rad- 


128 


100 


275 


7 


Innsbruck 1935-36 


inger and 










(2300 m msl) 


Dymek [47] 










New York 1941-42 


Hess [24] 


27 


97 


481 


10 


Oceans: 












Pacific Ocean 


Bauer and 

Swann [4] 


— 


3.3 


— 


— 


Subarctic 


Bauer and 
Swann 4] 


— 


0.4 


— 


— 


All oceans, far 


Mauchly [41] 


— 


1.2 


— 


— 


from continents 













* Approximate. 

monthly mean from spring to summer [39, 42, 43, 47]; 
however, in the valley at Innsbruck, the cold season 
(January) shows the highest Rn values. This apparent 
contradiction can probably be explained by the fact 
that the temperature influence upon the exhalation is 
opposed by the effect of the temperature lapse rate on 
the vertical transport of Rn. In other words, during 



the cold season the Rn content of the valley air may 
increase in spite of reduced exhalation because of very 
little vertical transport, whereas in simamer the effect 
of the austausch exceeds that of strong exhalation. 
Annual variations on mountaintops have not been 
measured as yet. 

There is a close relationship with meteorological 
influences: Falling pressure increases the Rn content, 
rising pressure decreases it [35, 39, 47], as is to be 
expected from the atmospheric influence upon the ex- 
halation. The influence of the wind is twofold: With 
increasing wind velocity there appears first an increase 
in Rn content (because of increased exhalation), then 
a decrease (because of predominance of upward trans- 
port over increased exhalation). The direction of the 
wind is also important inasmuch as air masses of mari- 
time origin show a smaller Rn content than those of 
continental origin [9]. Precipitation, particularly that 
of long duration, decreases the Rn content; this can 
easily be explained by a decrease of exhalation due 
to the clogging of the ground capillaries {e.g., [39]). 
Precipitation particles themselves show a measurable 
content of radioactive inductions [23] which they ap- 
parently acquire while falling; on the high seas they 
are practically inactive, as is to be expected [48]. 

Table V. Radon Exhalation of the Ground 







Exhalation 


Place 


Author 


(C cm-2 sec-" X 
10-1!) 


Dublin 


Smyth [55] 


74 


Manila 


Wright and Smith [60] 


21 


Liebenau/Graz 


Kosmatli 35) 


40 


Innsbruck 


Zupancic 63] 


23 


Innsbruck 


Zeilinger [61] 


50 

Mean: 40 



The fact that temperature inversion layers with a 
high aerosol content appear to be especially rich in Rn 
[9] would seem to indicate an austausch effect. On the 
other hand, this fact may also point to a causal rela- 
tionship such that, because of selective adsorption by 
the aerosol particles, the vertical distribution of Rn 
is essentially caused by the distribution of the aerosol 
[27]. 

Radon Balance of the Atmosphere. As has been men- 
tioned in the beginning, the gaseous emanations are 
the connecting links between the primary radioactivity 
of the ground and that of the atmosphere. By diffusion 
and the suction effect of the wind upon the ground 
capillaries, these emanations are brought into the at- 
mosphere where they are distributed to greater heights 
under the influence of vertical convection. Since, to- 
gether with their disintegration products, they have 
only a limited life-span, a height distribution, char- 
acteristic for each of the radioactive substances, must 
develop. 

The measurements undertalcen so far (see Table IV) 
show the expected decrease with height, but are not 
sufficient for the quantitative examination of this rela- 
tionship. However, there is another possibility of de- 



RADIOACTIVITY OF THE ATMOSPHERE 



159 



termining the balance (we restrict our examination 
to Rn). 

In the mean, the supply from the ground has to 
maintain an equilibrium with the rate of disintegration 
of Rn in the entire atmosphere. Let us disregard the 
variations in a horizontal direction and consider a 
vertical cohunn of air of one square centimeter cross 
section reaching to the top of the atmosphere; the 
following equation must then be fulfilled: 

;sx = E, 

where S is the entire Rn content of the column, X is the 
disintegration constant of i?n, and E is the exlialation. 
The total content S of the air coliram can be computed 
as 



S 



= / 

Jo 



s(h) dh, 



where s(h) represents the vertical distribution of Rn. 
For this function s{h) we may write the following 
differential equation: 

. (fs , dA ds . „ 

'^dh> + dhdh-'''''=^' 

in which p expresses the density of the air and A the 
austausch coefficient. 

Integrations of this equation have been carried out 
by Hess and Schmidt [25] for an austausch that is 
constant with height (dA/dh = 0), and by Schmidt 
[51] with corrections by Priebsch [46], and by Lettau 
[37] for various assumed values of an austausch coeffi- 
cient variable with height. Values for S and E as calcu- 
lated by these various authors are presented in Table 
VI. The agreement between these values and the ob- 

Table VI. Total Radon Content and Rate of Disintegra- 
tion OF A Vertical Column of Unit Cross Section and 
OF Atmospheric Height, after Various Authors 



Author 



Hess and Schmidt [25] 
A = 50 g cm~' see" 
A = 100 g cm"' sec~ 

Schmidt [51] 

(Priebsch [46]) 

Lettau [37] 




(C sec-' X 10-18) 



27 
38 

20 
57 



served exhalation of 40 X lO-'^ C cm-^ sec"' (Table V) 
can be considered entirely satisfactory. In smnmary it 
can be said that the emanation content of the atmos- 
phere over land and water can be completely understood 
if one considers the solid earth's crust as the almost 
exclusive source of emanation. 

Problems 

Our knowledge of radioactive substances in the atmos- 
phere is fairlj' complete as far as their identity, meas- 
urability, and origin are concerned. Less clear is the 
mechanism of the horizontal and vertical distribution 
of these substances in the atmosphere. As admixtures to 
the air, they take part in its movement and thus 



enable us to reach important conclusions regarding air- 
mass displacements. Therefore, if one considers the 
question of a suitable continuation of research, the 
use of radioactive air admixtures as tracers for special 
meteorological problems opens new possibilities. One 
experiment in particular suggests itself: the use of 
radioactive emanations as an indicator of austausch 
movements on the one hand, and for the determination 
of the life history of air masses on the other hand. 
Several of the above-mentioned investigations point 
in this direction; only a few will be mentioned. 

1. The vertical distribution of the individual radio- 
active component can be considered as the result of 
austausch [9, 25, 27, 37, 39, 46, 47, 51]; therefore, with 
proper measurements, it ought to yield, in turn, in- 
formation about its efficacy and vertical extent on the 
average as well as in single cases. 

2. Air that stagnates in the same climatic region for 
some time acquires, by contact with the ground, cer- 
tain characteristics which allow us to define it as an 
air mass of a given type. One must expect that the air 
mass also adopts different radioactive properties, ac- 
cording to the exhalation of the ground beneath. Thus, 
for instance, an air mass located over the ocean for a 
long time, will show a considerably smaller Rn content 
than air from the continent, as has been sho'mi by 
measurements of the author on the Dutch coast [30] 
(see Table IV). Furthermore, the pronounced activity 
differences w^hich Becker [9] has found above and below 
an inversion point to the effects of austausch or air- 
mass characteristics. 

3. The radioactivity of precipitation gives an in- 
dication of the radioactive character of the air mass 
from which it falls. The pronounced increase in ioniza- 
tion near the ground during thundershowers [15, 57] is 
probably due to an especially strong upward transport 
of low-level (and therefore more strongly radioactive) 
air in the formation of a thunderstorm and the return 
of the radioactive admixtures through precipitation. 

It is obvious that a more thorough investigation of 
these relationships from a meteorological and thus at- 
mospheric-electrical and bioclimatological point of view 
can become of great importance. 

The methodological problems, for example, consist of 
the following: 

1. The over-all substitution of measurement by auto- 
matic recording. 

2. A simultaneous survey of diurnal variations of the 
radioactive elements in the air at several stations at 
various altitudes. 

3. Attempts at an air-mass classification according 
to origin and age on the basis of the Rn content and the 
proportion of Ra- to T/i-derivatives. 

4. Vertical cross sections of the atmospheric radio- 
activity, perhaps by means of airplane measurements 
or b}^ testing the active deposits on the mooring cable 
of a captive balloon when bringing it in (using Geiger 
counters). 

5. Determination of the radioactivity of precipita- 
tion. 



160 



ATMOSPHERIC ELECTRICITY 



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35 



36 



37 



38. 
39. 



RADIOACTIVITY OF THE ATMOSPHERE 



161 



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Leipzig, Teubner, 1927. 

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freien Luft." Phys. Z., 32:622-629 (1931). 

47. Radinger, G., und Dymbk, P. L., "Untersuchungen 

liber den Radiumemanationsgehalt der Freiluft in Inns- 
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dans I'Antarctique pendant I'Expedition Charcot 
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Verteilung der Radiuminduktion in der Atmosphare 
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50. Satterly, J., "The Amount of Radium Emanation in the 

Atmosphere." Phil. Man., (6) 16:584-615 (1908); "On 
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51. Schmidt, W., "Zur Verteilung radioaktiver Stoffe in der 

freien Luft." Phys. Z., 27:371-378 (1926). 

52. Schwalb, K., "Beitrage zur Kenntnis der Radium-Emana- 

tion in der Atmosphare." Biokl. Beibl., 8:82-90 (1941). 

53. ScHWEiDLER, E. V., "Zusammenfassender Bericht uber 

die Beobachtungen an der luftelektrischen Station See- 
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Abt. Ila, 126:1009-1035 (1917); "Zusammenfassender 
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54. SiEGL, L., "tjber die quantitative Messung der Radium- 



emanation im Schutzringplattenkondensator." S. B. 
Akad. Wiss. Wien, Abt. Ila, 134:11-37 (1925). 

55. Smyth, L. B., "On the Supply of Radium Emanation from 

the Soil to the Atmosphere." Phil. Mag., (6) 24:632-637 
(1912). 

56. Swann, W. F. G., "The Measurement of Atmospheric Con- 

ductivity, together with Certain Remarks on the Theory 
of Atmospheric Radioactive Measurements." Terr. 
Magn. almos. Elect.. 19:23-37 (1914); "The Theory of 
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Discussion of the Theory of the Gerdien Conductivity 
Apparatus, and of the Theory of the Collection of Radio- 
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92 (1914); "On Certain New Atmospheric-Electric In- 
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Atmospheric-Electric Observations on the Third Cruise 
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57. Wait, G. R., and McNish, A. G., "Atmospheric Ioniza- 

tion near the Ground during Thunderstorms." Mon. 
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58. WiGAND, A., "Luftelektrische Untersuchungen bei Flug- 

zeugaufstiegen." Phys. Z., 25:684-685 (1924). 

59. und Wenk, F., "Der Gehalt der Luft an Radium- 
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60. Wright, J. R., and Smith, O. F., "The Variation with 

Meteorological Conditions of the Amount of Radium 
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the Air Exhaled from the Surface of the Ground, at 
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61. Zeilinger, p. R., "Ueber die Nachlieferung von Radium- 

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62. Zlatarovic, R., "Messungen des Radium-Emanations- 

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BiecJ., 39:33-46 (1934). 



CLOUD PHYSICS 

On the Physics of Clouds and Precipitation by Henry G. Houghton 165 

Nuclei of Atmospheric Condensation by Christian Junge 182 

The Physics of Ice Clouds and Mixed Clouds by F. H. Ludlam 192 

Thermodynamics of Clouds by Fritz Moller 199 

The Formation of Ice Crystals by Ukichiro Nakaya 207 

Snow and Its Relationship to Experimental Meteorology by Vincent J. Schaejer 221 

Relation of Artificial Cloud-Modification to the Production of Precipitation 

by Richard D. Coons and Ross Gunn 235 



I 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 

By HENRY G. HOUGHTON 
Massachusetts Institute of Technology 



INTRODUCTION 

The entire science of meteorology is concerned with 
the physics of the atmosphere, but the term physical 
meteorology has been accepted as the designation for 
onljr one portion of the science. This division of the 
field includes topics such as atmospheric optics, at- 
mospheric electricity, solar and long-wave radiation, 
and the phj^sical processes of condensation and pre- 
cipitation. The latter is the subject of the present con- 
tribution. The discussion will start with a consideration 
of condensation nuclei and will then proceed in turn to 
treat the initiation of condensation, the growth of the 
condensation products, and the formation of precipi- 
tation elements. A distinction must be made between 
condensation in the liquid phase and in the solid phase. 
There are also differences between the formation of 
solid and liquid precipitation elements. A brief dis- 
cussion of the artificial dissipation of fog will also be in- 
cluded. 

Some of these topics are discussed by other contri- 
butors to this volume.^ The purpose of the present 
contribution is to review the entire subject. For this 
reason no attempt will be made to avoid the topics 
covered by the other authors. Such duplication is not 
only essential to a complete discussion of the subject 
but may also serve to emphasize more clearly some of 
the different points of view held by various workers in 
the field. Continuity does not require a discussion of the 
artificial modification of clouds, and this topic has 
been omitted in view of the complete treatments in 
this volume by Coons and Gunn and by Schaefer. 

The subject of cloud physics has received much 
attention in recent years. This is due in large measure 
to the recent experimental work on the artificial modi- 
fication of supercooled clouds. Other stimuli have been 
the problems of aircraft icing, artificial fog dispersal, 
the propagation of microwave radio energy, and the 
detection of precipitation areas by radar. In sharp 
distinction to many other areas of meteorology, the 
problems of cloud physics are amenable to the tech- 
niques of the experimental physicist both in the labora- 
tory and in the free atmosphere. 

NUCLEI OF CONDENSATION 

The discovery of nuclei of condensation is generally 
attributed to Coulier who reported on them in 1875. 
The^ pioneer in this field was John Aitken [2] whose 
work on nuclei of condensation extended from about 
1880 to 1916. C. T. R. Wilson's name is usually coupled 
with Aitken's, but his work has proven to be of more 
value to particle physicists than to meteorologists. 



1. In particular, reference should be made to the papers by 
Coons and Gunn, Junge, Ludlam, Moller, Nakaya, and Schaefer. 



Once it was established that all natural condensation 
requires the presence of condensation nuclei, attention 
was focused on their source, nature, and size and on their 
distribution in time and space. Many of these questions 
are still in debate. Aitken studied the subject both in 
the laboratory and in the open air. His insight into the 
problem and his experimental techniques stand un- 
rivaled as monuments to his name in this field. He 
developed the expansion type of nucleus counter which 
has been used in one form or another by all subsequent 
workers in the field. The careful reading of Aitken's 
many papers [2] is an absolute requirement for any 
serious student of condensation nuclei. 

Source and Nature of Nuclei. Aitken [2] always 
referred to nuclei of condensation as "dust particles" 
although he stated clearly that they were distinct from 
the type of dust raised, for example, bj^ high winds. 
He felt that there were two types of nuclei, those with 
an affinity for water vapor on which condensation 
begins below saturation, and nonhygroscopic nuclei 
which require an appreciable degree of supersaturation 
for the initiation of condensation. In his opinion the 
first type is the true fog-former while the second type 
usually produces only haze. Using an Aitken "dust 
counter," Wigand [56] found that an artificial increase 
in the dust content of air, such as was produced by 
beating a carpet in a room, had no effect on the nucleus 
count. He concluded that such nonhygroscopic dust 
was inactive as condensation nuclei and proposed that 
the Aitken dust counter be renamed the kern counter, 
a suggestion that has been generally adopted. Wigand's 
conclusions were apparently supported by kern counts 
in the presence of sand and dust storms and bj^ Boylan's 
laboratory studies [5]. Boylan's results indicated that 
the introduction of dust such as coal dust and 
carbon black slightly decreased the kern count. He 
suggested that this was due to the sweeping action 
of the dust particles on the kerns. Later Junge [26] 
experimented with a wide variety of dusts, includ- 
ing some which are not wetted by water, and found 
that all dusts with a large number of particles smaller 
than about 10-m radius increased the kern count. He 
concluded that particles of any substance can act as 
nuclei of condensation. He argued that larger particles 
would fall out in the chamber of the kern counter before 
the expansion could be made. Junge felt that earlier 
investigators did not produce dusts with a sufficient 
number of small particles to increase the kern count 
significantly. As he pointed out, a dust cloud of several 
hundred large particles in a cubic centimeter looks 
much denser than so-called "dust-free" air, which may 
contain several himdred thousand ultramicroscopic con- 
densation nuclei per cubic centimeter. Junge's results 
are very convincing and it seems reasonable to accept 
his conclusions. On the other hand, the evidence still 



16S 



166 



CLOUD PHYSICS 



supports Aitken's conclusion that the hygroscopic nuclei 
are the important cloud producers and that neutral 
dust is of lesser importance. Boylan [5] found in Dublin 
that the number of kerns determined with the Aitken 
instrument averaged fifteen times the number of dust 
particles determined with the Owens impact dust 
counter, 

Aitken and many others have established that flames 
and burning materials form tremendous numbers of 
nuclei and also that heat alone, as from a heated plat- 
inum filament, will form nuclei in natural air. Aitken 
and also Coste and Wright [6] showed that nuclei could 
be formed by spraying sea water. The latter authors 
also found that fuming sulfuric acid was an active kern 
producer. Although flames produce a variety of products 
it has been established that substances containing sulfur 
are the most effective fuels. This is significant because 
of the sulfur content of coal. When sulfur is burned the 
nonhygroscopic dioxide is formed. This does not easily 
oxidize to the hygroscopic trioxide in air at normal 
temperatures. Aitken found that both ozone and hydro- 
gen peroxide are effective oxidizers of sulfur dioxide. 
He also claimed that ultraviolet solar radiation oxidized 
the sulfur dioxide. Coste and Wright [6] suggested that 
at temperatures above 620C, and in the presence of 
water vapor, hygroscopic nitrous acid is formed. This 
would explain the production of nuclei by hot filaments. 
They also suggested that the nitrous acid is the oxi- 
dizing agent for sulfur dioxide. 

There is general agreement that sea salts are effective 
as condensation nuclei. Sea-salt crystals have been 
observed in the atmosphere by Owens [43], Dessens 
[8, 9], and Woodcock and Gifford [57]. Kohler [27, 28] 
and others have demonstrated the presence of chloride 
ion and of other sea-salt anions in water from clouds, 
fogs, and rain. If the amount of chloride ion, for 
example, as measured in a bulk sample is divided by 
the number of drops, it yields a nucleus of reasonable 
size. Any object which has not been carefully cleaned 
exhibits the ubiquitous sodium flame when it is heated. 
On the other hand there is evidence which suggests 
that the sea is not the principal source of condensation 
nuclei. The number of nuclei is much smaller over the 
oceans than over the land. A minimum kern count of 
nearly zero has been observed over the ocean and the 
usual count is from several hundred to several thousand 
per cubic centimeter. Typical values over land range up 
to 100,000 in rural, and a million or more in urban areas. 
Simpson [49] shows that if all active nuclei come from 
the sea surface, the rate of nucleus production must be 
about 1250 sec~^ cm~^. This appears to be unreasonably 
large if the nuclei are formed by the evaporation of the 
spray resulting from wave action. A large proportion 
of the spray drops will be so large that they will fall 
back to the surface. Findeisen [12] holds that the sea 
salt indubitably present in the atmosphere is in the 
form of say 10-20 large particles of about 10""'° grams 
mass per liter of air. Although these are probably all 
active nuclei, their number is small compared to the 
total number of nuclei. Their presence would serve to 
explain the observed chloride content of cloud and 



rain water. There are isolated observations that the 
evaporation of sea water (without visible spray) pro- 
duces kerns, and Aitken found that nuclei were formed 
by the action of the sun on the foreshore at ebb tide. 
Attempts to identify the nucleus in an evaporating 
cloud drop under the microscope have failed. Dessens 
[8] has caught nuclei from the air on spider webs and 
caused them to grow into drops or to form crystals by 
varying the humidity. These are probably the relatively 
large sea-salt particles referred to by Findeisen [12]. 
Wright [58] has shown that visibility near the seacoast 
is a function of the relative humidity, which can be 
explained by assuming that the nuclei are hygroscopic. 
Wright felt that he had shown in this way that the nuclei 
in question were sea salts but Simpson [49] argued that 
his procedure did not permit the identification of the 
hygroscopic agent. 

It is generally concluded that most active conden- 
sation nuclei are hygroscopic particles and that the 
nonhygroscopic nuclei are unimportant. More infor- 
mation is required to explain this strong preference for 
hygroscopic nuclei. The hygroscopic and nonhygro- 
scopic kerns are presumably of about the same size; if 
anything, the hygroscopic nuclei are somewhat smaller. . 
It can be shown that the lowering of the vapor pressure 
by the salt is not of major importance, since a slightly 
larger nonhygroscopic particle will support condensation 
at the same degree of supersaturation. It appears from 
Volmer's work [52] that the wettability of the substance 
plays an important role. On a surface which is not 
wetted by water, condensation occurs in the form of 
small lens-shaped drops. The work required is greater 
than when the surface is wetted and increases with the 
contact angle between the water and the surface. 
Greater work for the phase change implies a higher 
supersaturation. Hygroscopic nuclei are liquid drops 
before cloudy condensation occurs and are therefore 
perfectly wetted. All other nonhygroscopic surfaces are 
less easily wetted and it may be that the nonhygro- 
scopic atmospheric dust is largely hydrophobic. Junge's 
finding [26] that paraffin spheres will serve as con- 
densation nuclei does not contradict this explanation 
since Volmer shows only that hydrophobic nuclei re- 
quire a greater supersaturation than hydrophilic nuclei. 
Junge did not report on the supersaturations used, but 
since he employed an Aitken' instrument it may be 
assumed that they were from 200 to 300 per cent. 
An extension of Junge's work with provisions for vary- 
ing the supersaturation would probably shed some 
light on this problem. 

The available evidence suggests that the hygroscopic 
nuclei are formed of sea salts and nitrous and sulfuric 
acids. Other hygroscopic materials may also be im- 
portant but it has yet to be shown that other such 
substances regularly exist in the atmosphere in suf- 
ficient quantity and in finely divided form. If it be 
assumed that sea-salt nuclei are formed only by the 
evaporation of spray, it must be conceded that the 
source is insufficient to supply a major fraction of 
atmospheric kerns. Further study on other possible 
mechanisms for the formation of sea-salt nuclei is 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 



167 



desirable. Perhaps rapid evaporation of sea water in the 
absence of spraj' forms nuclei. Aitken's observation that 
nuclei are formed by the action of sunlight on salt- 
water beaches should be followed up. Dessens [9] found 
that salt droplets become supersaturated when the 
relative humidity is decreased and finally crystallize 
explosivelj^ occasionally resulting in rupture. He ten- 
tatively offered this as a possible mechanism for the 
production of small condensation nuclei from the rela- 
tively large crystals formed when sea spray evaporates, 
but later expressed the opinion that the fracture 
mechanism is too rare to be of major importance. 

The sulfuric acid in the atmosphere must come pri- 
marily from the sulfur in coal, although volcanic activity 
may contribute a small amount. Much of the research 
on nuclei has been done in industrial areas such as the 
British Isles and Germany, so that the importance of 
sulfuric acid nuclei may have been overemphasized. 
Althovigh the high concentrations of nuclei in industrial 
areas is almost certainly due to the products of man- 
made combustion, no one believes that the cloud and 
precipitation regimes of the world have been greatly 
altered by industrialization. It appears that nitrous 
acid nuclei are also produced by combustion but here it 
is the high temperature which acts as a catalyst to form 
the nuclei from the natural constituents of the air. 
Forest fires are as effective for this as man's furnaces. 
It is also known that nitrous acid is formed by the 
action of lightning discharges. It may be that nitrous 
acid is the principal kern material and that the high 
kern-concentrations in urban areas are due to the 
products of combustion and are of only local impor- 
tance. Adel [1] and Shaw and collaborators [48] have 
obtained spectroscopic evidence of the presence of about 
1 cm of nitrous oxide at NTP in the atmosphere. 
There is no information on the vertical distribution of 
the nitrous oxide but these observations suggest that it 
is a universal constituent of the atmosphere. There 
may well be other substances, even nonhygroscopic 
ones, obscured by the abundance of other nuclei in 
industrial areas, which are the really important nuclei of 
the free atmosphere. 

Size and Size Distribution of Nuclei. The upper 
limit of nucleus size is set by the settling rate and also 
in some cases by the method of formation. As an 
example, the largest sea-salt nucleus probably has a 
diameter of the order of 5 X 10"^ cm. Because the work 
of subdivision of a solid or a liquid increases rapidly 
with the amount of new surface formed, the diameter 
of the smallest sea-spray nucleus or dust particle pro- 
duced by erosion or grinding is of the order of 10~^ cm. 
Diameters of nuclei formed from gases such as sulfuric 
and nitrous acids probably range from 10~^ to 10~^ cm. 
Such nuclei are not apt to be as large as sea-salt nuclei 
because of the small concentration of the gases from 
which they are formed. All sizes within these rather 
wide limits are to be expected. (For completeness it may 
be mentioned that small ions with dimensions of the 
order of 10~' cm will serve as nuclei only at four to five 
fold supersaturations and cannot play any role in 
natural atmospheric condensation.) 



Only the larger nuclei can be measured with the visual 
microscope. The electron microscope opens the way for 
the measurement of smaller nuclei if a means can be 
found for the collection of the nuclei on the stage of this 
instrument. Most measurements of the size of nuclei 
have been made by indirect means. The large or Lan- 
gevin ions of the atmosphere are generally believed to 
be condensation nuclei which have captured a small 
ion or an electron. Boylan [5] states that about 60 
per cent of the nuclei carry a single electronic charge 
and are identical with the large ions. The mobility 
(velocity in unit electric field) of such ions may be 
measured and their size computed from Stokes' law. 
Such measurements yield diameters in the neighbor- 
hood of 10~^ cm. 

As already mentioned, the size of the nucleus may be 
determined by assaying a bulk sample of cloud or fog 
water for the assumed constituent and dividing by the 
number of drops represented in the sample. This was 
done first by Kohler [27], who collected rime at a 
mountain observatory and determined the chloride con- 
tent by titration. The mean drop size was measured 
by the corona method. By assuming that the other 
anions of sea salt were present in the same proportion as 
in the sea, he computed the average mass of the nuclei 
to be 1.847 X 10~'* g, equivalent to a diameter of about 
5 X 10~* cm. This procedure is open to the criticism of 
Findeisen [12] that the salt might be in the form of a 
few relatively large particles. 

Direct measurements of the size of nuclei have been 
made by Dessens [9] and by Woodcock and Gifford 
[57]. Dessens caught the nuclei on spider threads and 
examined them with a visual microscope. He reported 
radii of nuclei ranging from 0.3 to 0.5 fi. The nuclei 
were in the form of drops at a relative humidity of 60 
per cent. There were others too small to measure, and 
also some larger ones. Woodcock and Gifford collected 
nuclei on glass slides 1 mm by 15 mm in size from an 
airplane flying over the ocean. The counts were cor- 
rected for the collection efficiency of the slides. They 
identified the nuclei as sea salts by determining the 
relative humidity at the transition between crystal and 
solution. They present their data in form of the mass 
distribution of the nuclei. The largest nuclei had a mass 
of about 2 X 10~^ g and the smallest a mass of near 
5 X 10~" g. These weights correspond to diameters of 
24 and 0.7 ju respectively at a relative humidity of 
80 per cent. When plotted on logarithmic paper. Wood- 
cock and Gifford's distiibution curves of nucleus mass 
versus number are nearly linear with negative slopes. 
Their method did not permit the collection of nuclei 
of mass less than 5 X 10~''' g. The total number of 
nuclei in a cubic centimeter of air was found to range 
from less than one to about thirty and to decrease 
rapidly with elevation in the first 300 m above sea 
level. Although no simultaneous measurements with an 
Aitken counter are reported, it is probable that the 
Aitken count would be large compared with that of 
Woodcock and Gifford. There is no evidence that these 
unmeasured nuclei are composed of sea salts. 

The methods outlined above of determining the size 



168 



CLOUD PHYSICS 



of nuclei yield the actual geometric diameter or mass. 
With the sole exception of the application of mobilitj^ 
measurements to large ion-nuclei, none of these methods 
can be used in the size range which includes the 
majority of the natural condensation nuclei of the 
atmosphere. An indirect measure of the effective size 
of condensation nuclei may be obtained by causing 
condensation to occur on them under controlled con- 
ditions. To discuss this procedure it is necessary to 
review briefly the theory of condensation on nuclei 
as first presented by Thomson [50] for neutral nuclei 
and Kohler [29] for hygroscopic nuclei. Thomson showed 
that the vapor pressure in equilibrium with a curved 
surface is greater than the vapor pressure in equilibrium 
with a plane surface at the same temperature. The 
supersaturation required to initiate condensation on the 
surface of a small sphere, which is wetted by water, is 
nearly inversely pi'oportional to the radius. This effect 
is illustrated by the upper curve in Fig. 1. The vapor 



IbO 

f 140 

5 

il30 

X 

>I20 

H 

H 

t- 




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\ 
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\ 
\ 
























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\ 


\ 




















inV 




r 


^ 


s^ 














uj'OO 

o 

(r 

a 90 

RO 








1 




f 


















io-«' 




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10" 



10° 10-° 10"^ 

RADIUS OF DROP IN CENTIMETERS 



10"- 



Fig. 1. — Growth curves of sodium chloride nuclei of masses 
as indicated at OC. The dashed line is for pure water drops. 

pressure over a solution of a hygroscopic salt is lower 
than that over pure water. In the case of a hygroscopic 
nucleus, both effects are in evidence and act in op- 
position. The net result is indicated by the lower curves 
of Fig. 1. The effect of the dissolved salt is dependent 
upon its concentration and thus is a function of the 
mass of the hygroscopic material and of the radius of 
the droplet. The Thomson effect is a function only of 
the radius of curvature. The three lower curves of 
Fig. 1 are for nuclei of sodium chloride of different 
masses as indicated on the curves. It is readily apparent 
that hygroscopic nuclei grow more slowly as the relative 
humidity increases toward saturation. In all cases, the 
growth curves reach a maximum in excess of 100 per 
cent relative humidity. This peak relative humidity 
must be exceeded if the nucleus is to become a cloud 
drop. The general behavior of these curves has been 
verified experimentally by Junge [25] who determined 
the size of hygroscopic nuclei at various relative hu- 
midities from the mobility of the nuclei as large ions. 
Wright [58] has obtained data on the variation of visi- 



bility with humidity which seem to confirm the general 
shape of the curves of Fig. 1 below saturation. 

The supersaturation corresponding to the maximum 
of the curves of Fig. 1 is a measure of the effective size 
of the nucleus. The geometric size can be determined 
only if the nature of the hygroscopic salt is known. 
An adaptation of the Aitken nucleus counter can be 
used to determine the effective size of the nuclei, as was 
shown by Junge [25]. He produced expansions of known 
and increasing amounts in a chamber and determined 
the number of drops after each expansion. In this way 
he obtained a nucleus spectrum. Earlier, Aitken [2] 
performed a similar experiment with his apparatus. 
The principal difference in the two techniques was that 
Junge used a large chamber and applied his successive 
expansions rapidly so that none of the previously acti- 
vated nuclei would evaporate. Aitken first produced a 
small expansion and counted the number of drops which 
fell out in the usual manner. He then proceeded to an 
increased expansion, waiting each time until the acti- 
vated nuclei had fallen out of the air. Aitken's pro- 
cedure is open to the objection that some of the drops 
might evaporate before falling out and thus leave 
nuclei to be counted again in subsequent expansions. 
Jimge's method involves the errors of counting the 
number of drops while they are suspended in the air. 
Most of Junge 's experiments were carried out with 
artificially produced nuclei, whereas Aitken used natural 
air. Qualitatively their results were very similar. The 
evidence is that a large number of nuclei are activated 
at the lowest expansion used, with smaller numbers 
requiring greater expansions or supersaturations. Aitken 
found that all of the ordinary nuclei in the samples of 
natural air were activated by a relative humidity of 
150 per cent. Further increases in the expansion 
ratio had no effect until the supersaturation required to 
produce condensation on small ions was reached. Junge 
found that 110 per cent relative humidity was sufficient 
to activate all of the nuclei in a sample of outdoor air. 

Number and Distribution of Nuclei. Literallj^ thou- 
sands of measurements of the number of nuclei in the 
air have been made with the aid of the Aitken instru- 
ment. As ordinarily used, this instrument produces a 
supersaturation of from 200 to 300 per cent and there- 
fore activates all natural nuclei but not small ions. 
As will be pointed out below, only a small fraction of the 
total number of nuclei are activated in natural con- 
densation processes. For this reason the total number 
of nuclei as determined by the Aitken counter is of 
limited value since no information regarding the size 
or the size distribution of the nuclei is obtained. A 
very complete summary of the measurements which 
have been made has been given by Landsberg [33], 
and no attempt will be made here to give any of the 
detailed results. The maximum concentration was found 
in cities, with an average of 150,000 per cubic centi- 
meter and a maximum of some four million. In the 
country, the average is of the order of 50,000 and the 
maximum near 400,000. Much lower concentrations 
are found over the oceans with an average of about 
1000 and a maximum of about 40,000. At a given 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 



169 



location, the concentration of nuclei has a diurnal and 
annual variation, the nature of which is largely de- 
pendent upon the local conditions. Correlations have 
been made of nuclei concentration with visibility, air 
mass, wind direction and force, and so forth. The im- 
portant question of the variation of the concentration 
of nuclei with elevation has not been thoroughly studied 
because of the difficulties in the way of such measure- 
ments. Most of these measurements have been made in 
mountainous regions at various elevations. These show 
a rapid decrease in concentration with elevation. A few 
determinations have been made from free balloons. 
These show a more rapid decrease of concentration of 
nuclei with increasing elevation than the mountain 
observations. The average vertical distribution of nuclei 
from the balloon ascents shows a count of 22,300 per 
cubic centimeter in the layer from to 500 m decreasing 
to 80 above 5000 m. Of necessity the balloon flights were 
made in anticyclonic weather, and the results cannot 
be considered typical of stormy conditions. In any 
event, the rapid decrease in concentration with in- 
creased elevation indicates that the source of conden- 
sation nuclei is at or near the surface. The nuclei are 
presumably carried aloft by turbulence and convection. 
This reasoning would suggest that the decrease in 
concentration with elevation would be smaller in cy- 
clonic than in anticyclonic conditions. No information 
is available on the change in size of the nuclei with 
elevation. It would be highly desirable to obtain more 
information regarding both the number and the size 
distribution of condensation nuclei in the free atmos- 
phere. 

THE INITIAL PHASE OF CONDENSATION 

Reference has been made above to the factors which 
control condensation on both hygroscopic and non- 
hygroscopic condensation nuclei. Referring again to 
Fig. 1, it is evident that condensation nuclei will not 
attain cloud drop size unless the supersaturation cor- 
responding to the maximum of the curves for hygro- 
scopic particles is exceeded. The magnitude of the 
supersaturation required is dependent on the mass of 
the hygroscopic material in the nucleus. The super- 
saturation required in the case of nonhygroscopic nuclei 
is dependent on the radius of curvature of the nucleus 
as indicated by the upper curve in Fig. 1. As was 
pointed out earlier, the critical supersaturation is prob- 
ably also dependent on how easily the surface of the 
nucleus is wetted. If the nucleus is composed of a 
microporous substance, condensation will occur at a 
lower relative humidity, the exact value depending on 
the size of the pores. Even in this case the nucleus 
cannot grow to cloud drop size unless some initial 
supersaturation occurs. It is therefore generally true 
that cloudy condensation cannot occur without a small 
degree of supersaturation. Such data as are available 
on the size and size distribution of nuclei indicate that 
the supersaturation required is usually less than one 
per cent. This is confirmed by the observation that the 
cloud base corresponds to the saturation level within 
the precision of the measurements. 



As the relative humidity exceeds 100 per cent, con- 
densation occurs first on the largest nuclei, that is, on 
those requiring the smallest amount of supersaturation 
to become active. Nuclei are said to be active when they 
have exceeded their critical supersaturations and are 
free to grow to cloud drop size. If the condensation is 
extremely slow, only the very largest nuclei will become 
active. As the rate of condensation is increased, the 
rate of condensation on the larger nuclei will not be 
sufficient to hold the supersaturation down and ad- 
ditional nuclei will be activated. This shows that the 
concentration of cloud drops is dependent primarily 
on the initial rate of condensation. 

The process which has just been described quali- 
tatively has been investigated theoretically and nu- 
merically by Kohler [29] and by Howell [24]. Kohler 
combined the radius of curvature effect and the effect 
of the hygroscopic solute with the thermodynamic 
equations of the condensation process. He did not 
introduce numerical values and did not consider the 
effect of a distribution of nuclear sizes. Howell assumed 
a broad spectrum of nuclear sizes and several different 
rates of condensation. He was able to show that only a 
very small fraction of the nuclei were activated and that 
under reasonable conditions the initial supersaturation 
was less than one per cent. He places the maximum 
probable supersaturation at about three per cent. By 
using different size distributions of the nuclei, Howell 
found that the concentration of cloud drops was much 
more dependent on the initial rate of condensation than 
on the size distribution of the nuclei. As soon as the 
initial stages of condensation are over, the supersatu- 
ration rapidly declines so that it is extremely unlikely 
that any additional nuclei will be activated. Because 
of the rapid decrease in supersaturation it is possible 
that a few of the smaller nuclei which were activated 
may evaporate. Howell contends that although this 
presumably occurs, the number of drops which start 
to form and then evaporate is very small compared to 
the total. It is reasonably safe to state that the con- 
centration of cloud particles immediately after the 
initial condensation is very nearly equal to the con- 
centration of activated nuclei and that there is little 
likelihood of an increase in the concentration of the 
cloud particles thereafter. 

GROWTH OF CLOUD DROPS 

When the initial phase of the condensation process is 
completed, the dissolved hygroscopic material and the 
radius of curvature have a relatively small effect on 
the further growth of the drop. The steady-state dif- 
fusion equation for the growth of drops as given by 
Houghton [21] is 

A(a2) = 8/c(p,„ - po„>) M, (1) 

where A (a-) is the increment of the square of the drop 
diameter in the time A/, p,, is the water vapor density 
at a distance from the drop, and po,,, is the density of 
water vapor in equilibrium with the drop. As pointed 
out by Howell [24], this equation is not valid during 
the initial condensation phase nor for very small drops 



170 



CLOUD PHYSICS 



but it may be used to determine the eiTects of con- 
tinued condensation on the size and size distribution 
of the cloud drops. The latent heat of condensation is 
released at the drop surface and transferred to the air 
by conduction. As a result the equilibrium temper- 
ature of the drop is greater than the air temperature 
and pow is therefore greater than the saturation water 
vapor density at the temperature of the air. Since 
(pw — pow) is always positive, supersaturation must 
exist throughout the condensation process. Compu- 
tations show that the supersaturation can hardly ex- 
ceed a few tenths of one per cent for any reasonable 
rate of lift. As a result of the parabolic relation between 
the drop diameter and the time in equation (1) the 
drop diameters will become more uniform as the con- 
densation proceeds. This conclusion has been verified 
by Howell [24]. 

Howell [24] attempted to find the conditions most 
favorable to a broad distribution of cloud drop sizes 
but was unable to delineate them in a clear-cut fashion. 
Slow cooling was expected to allow the initial effects 
of the solute and radius of curvature to exercise a 
maximum effect in broadening the size of the distri- 
bution. The small number of nuclei activated largely 
compensated for any such broadening. Rapid cooling 
had the opposite effect and it appears that some inter- 
mediate rate of cooling will yield the broadest drop- 
size distribution. The computed drop-size distributions 
are of the same general form as those observed in 
natural clouds, but are quite narrow, corresponding 
to the more homogeneous half of the clouds measured 
at Mount Washington, New Hampshire. It does not 
seem possible to explain the broader size distributions 
often observed by a uniform lift process of the type 
treated by Howell. This conclusion appears to be 
definite, in spite of incomplete knowledge of the con- 
densation nucleus size spectrum, because of the con- 
trolling effect of the initial rate of condensation. 

Some other mechanism must be sought to explain 
broader size distributions than those which result from 
uniform lift. Arenberg [3] suggested that turbulence 
would bring condensation products of different histories 
into the same region, thus resulting in a broad size 
distribution. Arenberg also suggested that the alternate 
up and down excursions of the drops in a turbulent 
atmosphere might lead to a broadening of the size 
distribution. However, excluding the evaporation dur- 
ing the descending branches of the motion, turbulence 
tends to narrow the size distribution and its net effect 
is apt to be small. 

In nature the uniform lift process adopted by Howell 
[24] for his computations is subject to important modi- 
fications. The rate of lift of different samples of the 
air at the condensation level will not be the same. 
Because of the controlling influence of the rate of lift on 
the concentration and size of the cloud drops it is to be 
expected that the mean drop sizes of the samples will 
show a rather wide range. Subsequent mixing of these 
samples by turbulence will result in a size distribution 
broader than that produced by a uniform lift. It is to 
be noted that fine-grain turbulence is required for the 



final intimate inixing essential to the broadening of the 
local drop-size distribution. It seems probable that 
any observed drop-size distribution can be explained 
on the basis of a suitable variation in the rates of con- 
densation of separate air parcels and their subsequent 
mixing. No data are available on the distribution of 
vertical velocities at the condensation level, so that a 
quantitative verification of this theory is not possible. 
Advective marine fogs also have broader drop-size 
distributions than might be expected from uniform 
cooling at the initiation of condensation. Such fog is 
formed at a much slower rate of cooling than any type 
of cloud. One anticipated result is that the drop con- 
centration in advective marine fogs is much smaller 
than in clouds. The cooling is produced at the under- 
lying surface and even in the usual stable stratification 
the mechanical turbulence is apparently sufficient to 
produce a range of cooling rates at the initiation of 
condensation. Such data as are available suggest that 
the drop-size distribution of radiation fog is quite 
narrow, presumably as a consequence of the more 
stagnant conditions of formation. 

The breadth of the drop-size distribution in clouds 
has an important bearing on the stability of the clouds 
and on the release of precipitation in clouds which do 
not reach the freezing level. It is important that further 
studies of the factors which determine the breadth of 
the distribution be undertaken. It appears that knowl- 
edge of the growth of the drops from condensation 
nuclei to large cloud drops is now well understood from 
the physical point of view. The missing information is 
concerned with those details of the air motion which 
determine the initial rate of cooling and the mixing of 
condensation products with diverse histories. 

Equation (1) shows that the time required for a drop 
to grow by condensation increases with the square of 
the drop diameter if the supersaturation is constant. 
This suggests that the maximum size of a condensation 
drop can be estimated by selecting a maximum time and 
a suitable supersaturation. An analysis of the drop 
growth process shows that the supersaturation reaches 
its maximum at the activation of the nucleus and 
thereafter rapidly declines, adjusting itself so that water 
will be condensed at the rate called for by the rate of 
lift. It is thus impossible to select an appropriate 
supersaturation for the computation of the maximum 
drop size. The factors that truly determine the maxi- 
mum drop size are the drop concentration and the 
amount of water vapor available for condensation. 
The former is dependent on the initial rate of conden- 
sation, the latter on the water-vapor content of the air 
and the total lift. It is now known that a considerable 
amount of unsaturated air from the environment is 
entrained by the rising column in cumulus convection. 
This desiccates the rising air and thus reduces the 
maximum drop size. Large drops are favoi'ed by slow 
initial lift, large water-vapor content, and large total 
hft. These factors are not all mutually compatible, so 
that the actual maximum drop size is considerably 
smaller than that computed for optimum values of 
each of the separate factors. It is generally believed 



I 



ON THE PHYSICS OP CLOUDS AND PRECIPITATION 



171 



that the practical maximum diameter reached by con- 
densation is about 100 to 200 ix. 

OBSERVATIONS OF DROP SIZE 
AND LIQUID WATER 

Methods of Measurement. Although a complete dis- 
cussion of methods of measuring cloud drop size and 
liquid-water content is beyond the scope of this article, 
some understanding of the measuring techniques is 
essential to a proper evaluation of the data. The most 
frequently used method of measuring cloud drop size 
has been the corona method. The angular diameter of 
the first- and higher-order diffraction rings obsei'ved 
around a light source is a measure of the average drop 
size. The method is theoretically unsound for drop di- 
ameters less than about 10 m- Although the possibility 
of determining the drop-size distribution by the corona 
method exists, no satisfactory technique has been de- 
veloped. The method is most applicable to the meas- 
urement of the drop size in homogeneous clouds; the 
coronas become diffuse and difficult to measure when 
the drop-size distribution is broad. 

Mean drop size and some indication of drop-size 
distribution can be obtained from the rotating multi- 
cylinder. This instrument consists of a series (often 
five) of cylinders of different diameter arranged to be 
slowly rotated with the axes of the cylinders normal to 
the wind. The collection efficiency of a cylinder is 
dependent on the air speed, the cylinder diameter, 
and the drop diameter. The numerical relations between 
these quantities and the collection efficiency have been 
determined by Langmuir and Blodgett [35]. From a 
comparison of the relative collections of the several 
cylinders the mean drop size and a measure of the 
drop-size distribution may be obtained. The liquid- 
water content (mass of liquid water in a unit volume of 
air) also may be determined from the measurements. 
This technique has been used at Mount Washington, 
New Hampshire (where it was developed by Arenberg), 
and on aircraft. It was first used only in supercooled 
clouds where the deposit is in the form of rime but 
absorbent cylinders are now used at temperatures above 
freezing. In order to obtain measurable collections the 
cylinders must be exposed to a few miles of cloud. For 
this reason the method yields only average values and 
cannot indicate rapid changes in drop size. In order 
to obtain a drop-size distribution it is necessary to 
assume the general form of the distribution curve. 

The most dii-ect means for the measurement of drop 
size and drop-size distribution is the collection and 
photomicrography of a sample of the drops. Direct 
photography of the drops in the air has so many in- 
herent difficulties that it cannot be considered to be a 
practicable method. The usual technique is to expose a 
suitably coated slide to the windstream and take photo- 
micrographs of the collected drops. Each drop image 
must be measured individually, and from one hundred 
to several hundred drops must be so measured to secure 
a representative distribution curve. The slide surface is 
covered with a hydrophobic surface, with an oil layer, 
or it is smoked. If the oil film is used, the drops are 



immersed thus retarding evaporation and preserving 
their spherical shape. On the smoked slides the drops 
leave clear areas which are related to the drop size. 
The drops on the hydrophobic surface are semiflattened 
and are subject to evaporation. Because of the finite 
size of the slides there is discrimination against the 
smaller drops. In addition, large drops tend to fracture 
on impact at high air speeds. In spite of these difficulties 
this general method is the only one which permits the 
nearly instantaneous determination of the drop-size 
distribution. 

It is clear, even from this brief discussion, that none 
of the present techniques is entirely satisfactory. It is 
not believed that improvements in any of the existing 
techniques will remedy this situation. A new approach 
to the measurement of drop size and size distribution is 
badly needed. 

Drop-Size Measurements. Kohler [30] has reported 
on the results of a large number of corona measurements 
of drop size made at a mountain observatory in 
northern Norway. Similar measurements have been 
made by others but Kohler 's work may be taken as 
representative. Kohler made several thousand indi- 
vidual measurements in mountain fog, stratus, strato- 
cumulus, and altocumulus. The absolute range of mean 
drop diameter was about 5 to 70 fi. The most frequent 
diameter was found to be about 17.6 n. He found that 
the range of the most frequent diameter was smaller for 
altocumulus and stratocumulus than for fog and stratus. 
Kohler's measurements yield no information on the 
size distribution, although he notes that some of the 
coronas were sharper than others; the sharper coronas 
corresponded to the narrower size distributions. 

Kohler has claimed that his data show what he calls 
a "mass grouping" such that the sizes in a group 
represented by ci = rfo(2)"'^ n= ±1, 2, 3, etc., are 
predominant. Here do is the constant modal diameter of 
the group and d represents the diameters of the drops 
composing the group. Other investigators have reported 
similar groupings. If this result were accepted, it would 
imply that there is a rather fixed drop size resulting 
from condensation and that other sizes are formed by 
the combination of drops of this initial size. This does 
not seem reasonable on physical grounds. No such 
grouping has been found in the multicylinder or micro- 
scopic data. It seems that Kohler's results must be 
due to some peculiarity of the corona technique and it is 
no longer believed that such a mass grouping exists. 

A large amount of data on drop size, size distribution, 
and liquid-water content in clouds has been collected 
at Mount Washington, New Hampshire [.51]. All three 
of the methods described above have been utilized but 
the bulk of the data has come from the rotating multi- 
cylinder. The mean drop diameter was found to be 13 
n, which is somewhat smaller than Kohler's 17.6 ix. 
The observed range of median diameter was about 5 
to 40 /i. It should be noted that the multicylinder mean 
diameter is a volume median such that one-half of the 
water is in smaller drops and one-half is in larger drops. 
The diameter obtained from the corona method prob- 
ably corresponds to the most frequent size. With the 



172 



CLOUD PHYSICS 



usual type of size-distribution curve the volume-median 
diameter is larger than the most-frequent diameter. 

As already stated, an indication of the breadth of the 
drop-size distribution can be obtained from the multi- 
cylinder data. The general form of the distribution 
curve must be assumed. The evidence available sug- 
gests that the majority of drop-size-distribution curves 
are of the general form assumed although there are 
occasional curves with multiple maxima. For conven- 
ience, nine standard volume-distribution curves have 
been adopted, identified by the letters A through J 
(I is omitted). The A distribution corresponds to com- 
plete uniformity and the succeeding letters to dis- 
tributions of increasing breadth as shown in Table I. 

Table I. Standard Volume-Distribution Curves Used in 

THE MULTICYLINDER METHOD 



Per cent of 

liquid water 

in each 


Ratio of diameter of group to volume-median diameter 
for each distribution 


group 


A 


B 


C 


D 


E 


F 


G 


H 


/ 


5 
10 

20 
30 
20 
10 
5 


1.0 
1.0 
1.0 
1.0 
1.0 
1.0 
1.0 


.56 
.72 
.84 
1.00 
1.17 
1.32 
1.49 


.42 
.61 
.77 
1.00 
1.26 
1.51 
1.81 


.31 
.52 

.71 
1.00 
1.37 
1.74 
2.22 


.23 

.44 
.65 
1.00 
1.48 
2.00 
2.71 


.18 
.37 
.59 
1.00 
1.60 
2.30 
3.30 


.13 
.31 
.54 
1.00 
1.73 
2.64 
4.02 


.10 
.27 
..50 
1.00 
1.91 
3.04 
4.93 


.06 
.19 
.42 
1.00 
2.22 
4.01 
7.34 



As will be seen from Table I, each distribution is 
made up of seven different drop diameters each repre- 
senting the percentage of the total water indicated in the 
first column. The drop sizes are represented as the 
ratios of the drop diameter to the volume-median 
diameter so that the distributions may be applied to 
any volume-median diameter. The frequency of oc- 
currence of the nine drop-size-distribution types at 
Mount Washington for the months November 1946 
through May 1947 is indicated in Table II. 

Table II. Occurrence of Drop-Size-Distribution Curves 
BY Type at Mount Washington, N. H. 



Distribution curve 
type 


A 


B 


C 


D 

21 


E 

13 


F 

5 


G 
2 


H 

4 


r 






Number of 
occurrences 


241 


96 


47 


7 



The predominance of narrow size distributions is 
striking. This is probably due in part to the high 
frequency of cloud-cap conditions which do not favor 
the nonuniform rates of lift apparently required to 
produce broad size distributions. For this reason Table 
II cannot be taken as typical of the clouds of the free 
atmosphere. It is also apparent from Table II that a 
significant number of broad distributions occur {E 
through J) which certainly cannot be explained on the 
basis of uniform lift. 

Multicylinder observations were also used to compute 
the liquid-water content. For the winter season 1945- 
46 the mean liquid-water content was 0.472 g m~^. 
The most frequent value was 0.24 g m^^ and the range 
was to 1.44 g m~^ There is a tendency for the higher 
liquid- water contents to be associated with higher tem- 



peratures. There is a similar tendency for the drop size 
to increase with the temperature. 

An extensive series of in-flight measurements of the 
liquid-water content and drop size of supercooled clouds 
has been made by the National Advisory Committee 
for Aeronautics and reported by Lewis and collabo- 
rators [37,38,39]. The principal instruments used were 
the rotating multicylinder, a rotating disc icing-rate 
meter, and a fixed cylinder which gives a measure of 
the maximum drop size. The measurements were made 
during three winter seasons and in both the eastern 
and the western portions of the United States. Although 
identification of the cloud type was made in each case 
it was found that, in general, the data did not warrant 
a more detailed classification than the distinction be- 
tween cumuliform and stratiform clouds. For three 
winter seasons the average volume-median drop di- 
ameter was found to be 20.5 n for cumuliform clouds 
and 14.7 n for stratiform clouds. The range of volume- 
median diameters was 3 to 56 /i for cumulus clouds 
and 3 to 50 /n for stratiform clouds. Nearly 50 per cent 
of the size distributions as determined from the rotating 
multicylinder were type A. Evidence is presented that 
the size-distribution data are unreliable and the authors 
feel that this technique is not applicable to in-flight 
measurements. By comparison of the simultaneous ob- 
servations of volume-median diameter and maximum 
diameter they concluded that the clouds are more 
homogeneous than is indicated by the rotating multi- 
cylinder. 

The liquid-water contents reported by Lewis and 
collaborators [37, 38, 39] ranged from 0.02 to 2.0 g m-^ 
for cumuliform clouds and from 0.01 to 0.7 g m~' for 
stratiform clouds. The average values for the three 
winter seasons were found to be 0.51 g m~^ for cumuli- 
form clouds and 0.134 g m~^ for stratiform clouds. 

In considering these data it must be remembered 
that they are winter values and that the temperatures 
were always below freezing and usually markedly below. 
The data presented show that both the drop size and 
the liquid-water content tend to increase with the 
temperature. The mean drop diameter obtained from 
these in-flight measurements is significantly larger than 
the Mount Washington mean. Again, this is probably 
due to the prevalence on the mountain of cloud caps 
which are presumed to contain smaller drops as a result 
of the rapid lifting. There is no significant difference in 
the liquid-water observations in flight and on Mount 
Washington. 

Diem [10] has reported the most extensive set of 
drop-size-distribution data from the free atmosphere. 
His measurements were made from aircraft by exposing 
a small oil-covered slide to the air stream for about 
Mo sec. The slides were photomicrographed within a 
minute of collection. The slides undoubtedly discrimin- 
ated against the smaller drops. Diem states that the 
collection was satisfactory down to a diameter of 3 /u 
but there is reason to believe that the discriminatory 
effect started at a somewhat larger diameter. Diem 
gives the most frequent drop diameters for six cloud 
tj^pes (Table III). Fair weather cumulus, altostratus 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 



173 



and stiatocumulus show the sharpest distributions. The 
other three cloud t^ypes exhibit broad size distributions. 
It is interesting to note that, in general, the cloud types 

Table III. D.\t\ from Composite Drop-Size-Distribution 

CURVE.S 

{After Diem [lO]) 



Cloud type 


Peak 
diameter (m) 


Range of 
curve ()i) 




14.5 
8.5 
7.9 
13.2 
12.9 
10.6 


3-40 


Fair-weather cumulus. . . 


2-20 


Stratoeumulus 

Nimbostratus 

Stratus 

Altostratus 


2-24 
2-42 
2-42 
2-30 







associated with precipitation have broad distributions. 
Verj' few of Diem's size distributions would fall in 
types A and B of Table I. The difference between 
Diem's data and the Mount Washington data in this 
respect is doubtless due in part to the different methods 
of measurement, but the writer feels that much of the 
difference is real. As pointed out above, there is good 
reason to believe that the conditions of formation of the 
Mount Washington cloud cap favor a narrow drop- 
size distribution. Until more data from the free atmos- 
phere are available it seems reasonable to accept Diem's 
data as typical rather than that from Mount Wash- 
ington. 

Drop-size measurements were made in sea fog by 
Houghton and Radford [22] on the northeast coast of 
the United States. The fog drops were collected on 
slides with a hydrophobic surface and then photomicro- 
graphed. Sampling errors occurred for drops smaller 
than about 20 m but this did not greatly affect the 
results in view of the relatively large drop size. The 
volume-median drop diameters ranged from 25 to 75 
IX with an average of 45 ju. The drop-size distributions 
appear rather broad because of the large drop size but 
most of them correspond to the C distribution of Table 
I, while a few B and D distributions also occurred. 
The largest drop measured was 120 ix in diameter. The 
mean liquid-water content was found to be 0.13 g m"' 
with a range of from 0.01 to 0.30 g m~'. 

The most striking feature of these results is the large 
size of fog drops as compared to cloud drops and the 
relatively small variation in the volume-median di- 
ameter and in the breadth of the size distribution. 
Coupled with the large drop size the relatively low 
liquid-water content shows that the drop concentration 
is very small. This suggests that the fogs observed 
formed on a few relatively large nuclei of condensation 
which quite possibly were sea-salt particles. Chemical 
analyses of the fog water tended to confirm this con- 
clusion. The chloride content of the water averaged 
70 parts per million and ranged from 8 to 480 parts 
per million. In fog water there appeared to be more 
sulfate ion in proportion to chloride than there was in 
sea water. This suggests the presence of some nuclei 
of industrial origin but does not prove that such prod- 
ucts served as nuclei. 

Hagemann [18] obtained drop-size distributions in 



fog in Germany using an adaptation of the oil-covered 
slide technique. He found that the most frequent size 
ranged from 9- to 34-/.1 diameter with an average of 
15.6 ti. As pointed out earlier, the volume-median 
diameter is always greater than the most-frequent di- 
ameter, so that Hagemann 's data do not differ greatly 
from those of Houghton and Radford [22]. Although 
data are irot available it is to be expected that the drop 
size in urban fogs would be smaller than in fogs formed 
in relatively clean air. 

Although more data on the drop-size distribution in 
clouds of the free atmosphere are badly needed, the 
information at hand is sufficient to give a good general 
idea of the end results of natural condensation processes. 
The most important conclusion is that most clouds of 
the free atmosphere, especially those associated with 
precipitation, have drop-size distributions broader than 
is explicable by a uniform lifting process at the con- 
densation level. As already indicated, the most promis- 
ing explanation for such a broad distribution is non- 
uniform rates of lift at the condensation level combined 
with later turbulent mixing. 

THE ICE PHASE 

Supercooled Water. The regular existence of super- 
cooled water clouds in the atmosphere is now a matter 
of common knowledge. Water clouds are much more 
common than ice clouds at temperatures down to 
— IOC and they have been observed down to — 35C 
and possibly below. Dorsey [11] and others have shown 
that water in bulk may be supercooled from a few 
degrees to as much as 20 degrees. The temperature at 
which water freezes spontaneously is not Ivnown with 
certainty, but theoretical considerations suggest that 
it is in the neighborhood of — 70C. Dorsey found that 
sealed samples of water had characteristic and repro- 
ducible freezing temperatures. The freezing temperature 
was found to be lower for the cleaner samples such as 
conductivity water than for natural water from ponds 
and puddles. Prolonged ageing, or heating to 97C, w^as 
found to lower the freezing temperature. Samples main- 
tained a few degrees below their characteristic freezing 
temperature remained unfrozen indefinitely. Dorsey 
concluded that his results were best explained by the 
assumption that freezing is initiated by "motes" of 
submicroscopic size. 

Rau [45] and Heverly [19] have investigated the 
freezing of supercooled water drops. Heverly reported 
that the freezing temperature was constant at — 16C 
for drops larger than 400-// diameter and decreased 
rapidly with the diameter for smaller drops with a 
suggestion of a minimum near — 40C for very small 
drops. Rau repeatedly froze a group of 24 drops and 
found a distribution of freezing temperatures which was 
apparently independent of drop size. The first two or 
three freezings lowered the average freezing temper- 
ature which thereafter remained constant. Other un- 
published investigations have yielded results similar 
to Rau's and it must be concluded that Heverly 's 
findings were in some way influenced by the experi- 



174 



CLOUD PHYSICS 



mental technique. Schaefer [46] has found that a super- 
cooled fog may be converted to an ice-crystal fog by 
cooling a portion of it to — 39C. HoUstein, quoted by 
Weickmann [55], studied the freezing of drops of sodium 
chloride solution of various concentrations. She found 
that the freezing point of the solution was equal to the 
freezing point of the water solvent minus the computed 
lowering of the freezing point due to the solute. There 
was some suggestion that the lowest possible freezing 
point of a sodium chloride solution lies in the neigh- 
borhood of — 35C at which point the salt may act as a 
freezing nucleus. 

Condensation and Sublimation Below OC. The ice 
phase may appear in the atmosphere either by the 
freezing of the liquid or by the direct sublimation of the 
vapor to the solid phase. Wegener [54] first suggested 
that the atmosphere contained sublimation nuclei which 
would act in a fashion analogous to condensation nuclei 
to promote sublimation in the vicinity of ice saturation. 
Findeisen [13] expanded on this concept and based his 
precipitation theories, in part, on the existence of such 
nuclei. It was assumed that sublimation nuclei were 
small solid particles of a shape similar to an ice crystal. 
Sublimation should occur on a nucleus truly isomorphic 
with ice at ice-saturation. 

The search for sublimation nuclei has been conducted 
by two experimental techniques. The first of these 
employs the expansion chamber and the second the 
dew-method in which the processes are observed on a 
chilled surface. Cwilong [7] used an expansion chamber 
of the Wilson-type which could be refrigerated. After 
the air was cleaned by repeated expansions, he found 
that a cloud of ice crystals was formed when the mini- 
mum temperature during the expansion fell below 
— 41.2C. He felt that small ions were acting as sub- 
limation nuclei below this temperature since the ice 
cloud formed at smaller expansions than those used to 
clean the air. In uncleaned outdoor air the transition 
temperature rose to — 32.2C and to — 27C when tobacco 
smoke was added. Cwilong also reported that at — 70C 
there was a distinct change, in that a small shower of 
quite large grains of ice accompanied the cloud of 
crystalline dust. Foui-nier d'Albe [17] repeated and ex- 
tended Cwilong's experiments with similar apparatus. 
He was unable to get the dense ice cloud in cleaned air 
below — 41C reported by Cwilong but confirmed the 
latter's conclusion that only liquid drops are formed 
above this temperature. Fournier d'Albe also found 
that no ice crystals were formed until water-saturation 
was reached or exceeded. He concluded that the ice 
phase was attained via the liquid phase and suggested 
that the particles be called freezing nuclei rather than 
sublimation nuclei. He also investigated the action of 
several types of artificial nuclei, including silver io- 
dide, which Vonnegut [53] had reported as causing 
the crystallization of supercooled clouds. Fournier 
d'Albe found that silver iodide nuclei caused ice crys- 
tals to appear at — 7C, but only at water-saturation. 
Other artificial nuclei such as sodium chloride, sodium 
nitrate, caesium iodide, and cadmium iodide were found 
to have no effect on the water-ice transition temper- 



ature. It is to be noted that the latter two substances 
form crystals with lattice constants similar to ice. 
It was on this basis that Vonnegut selected silver io- 
dide. On the other hand a water-drop cloud formed on 
cadmium iodide and then evaporated left nuclei on which 
ice formed at ice-saturation. This suggests that the 
nuclei of silver, caesium, and cadmium iodides used by 
Fournier d'Albe may not have been in crystalline form. 

Findeisen and Schulz [16] used a much larger ex- 
pansion chamber with a volume of 2 m^, which was 
arranged to permit expansions at rates comparable to 
those in nature. Their results were similar to those of 
Cwilong and Fournier d'Albe in that the clouds formed 
by steady expansions were invariably water or mixed 
water-ice clouds even at a temperature of — 40C. On 
some occasions when the expansion was interrupted 
just prior to the attainment of water-saturation, ice 
crystals were formed in the absence of a water cloud. 
At an expansion equivalent to a vertical velocity of 
5 m sec~^ ice crystals were first observed at about 
— 7C and their number increased with decreasing tem- 
perature. In the neighborhood of — 35C a very large 
increase occurred. At more rapid expansions the first ice 
crystals appeared at lower temperatures but the sudden 
increase occurred at a temperature somewhat higher 
than — 35C. All of these experiments were performed 
in uncleaned surface air. Very similar results were ob- 
tained by Palmer [44], who observed the formation of a 
few ice crystals at — 22C and at a relative humidity 
of 97 per cent with respect to water. He also observed 
a rapid increase in ice crystals at — 32C in natural 
surface air. In airplane flights, with a smaller expansion 
chamber. Palmer found the — 32C nuclei only below 
the haze inversion; at higher altitudes the first crystals 
appeared at from — 41C to — 44C. 

The most extensive investigations of condensation, 
free2;ing, and sublimation on a chilled surface have been 
made by Weickmann [55]. The advantages of this 
technique are that the individual particles may be 
viewed with a high-power microscope, that the tem- 
perature and rate of cooling may be controlled pre- 
cisely, and that the supersaturation with respect to ice 
is known at all times. The disadvantage is that the 
condensation occurs on a surface rather than in the air. 
Weickmann showed rather conclusively that the effect 
of a properly cleaned surface was small. Weickmann 
worked mostly at or near — 40C. He found that ice 
crystals formed only when water-saturation was ap- 
proached. In one series of ten tests, using nuclei from 
a heated room, ice crystals formed at an average water 
relative humidity of 97 per cent, the range being from 
93 to 104 per cent. Using the residue from evaporated 
drops as nuclei, a few crystals formed after 33 minutes 
at relative humidities of from 85 to 90 per cent wth 
respect to water or from 120 to 130 per cent with respect 
to ice. At or above 100 per cent water relative humidity 
thousands of ice crystals formed at once. A few sub- 
stances were found which favored the formation of ice 
at higher temperatures or lower ice-supersaturations, 
but in no case were crystals formed near ice-saturation. 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 



175 



No ice formed on soluble nuclei even at low temper- 
atures; it appeared that solid nuclei were required. 

Weickmann and others [55, 31, 32] also considered 
the problem from the theoretical side and showed that 
the structure of the ice crystal is so unique that it is 
extremely unlikely that any substances exist in the 
atmosphere which are truly isomorphic with ice. Weick- 
man concluded that the atmospheric ice phase is formed 
by the freezing of the liquid on solid freezing nuclei. 
He felt that the freezing nuclei were often condensation 
nuclei with a microporous or fissured surface which pro- 
moted condensation. He conceded that sodium chloride 
nuclei might act as freezing nuclei at temperatures 
below — 35C. Although he observed a few nuclei on 
which ice formed below water-saturation, he preferred 
to call all of the nuclei freezing nuclei rather than 
sublimation nuclei. 

There are still many unanswered questions regarding 
the formation of ice crystals in the atmosphere, but 
some tentative conclusions can be formed. It seems 
clear that at all temperatures down to about — 40C 
liquid condensate is more common than ice. Almost all 
investigators found a critical or transition temperature 
near — 40C although mixed water-ice clouds have been 
reported both in the free atmosphere and in the labora- 
tory down to at least — 50C. The latter measurements 
may be in error and should be checked. It should not be 
concluded without further information that — 40C is a 
spontaneous freezing temperature. Since all drops or 
crystals probably form on some type of nucleus this 
may be the temperature at which the small soluble 
condensation nuclei act as freezing nuclei. The com- 
puted spontaneous freezing temperature of — 70C is 
based on physical constants, the values of which are not 
accurately known. 

It is probably true that there are no atmospheric 
nuclei on which sublimation occurs at or below ice- 
saturation. It has been concluded from this that there 
are no true sublimation nuclei in the atmosphere except 
ice itself. On the other hand, ice crystals have been 
formed below water-saturation, although at consider- 
able supersaturations with respect to ice. In the opinion 
of the writer it is not proper to require that a subli- 
mation nucleus be active at ice-saturation. Many solid 
condensation nuclei do not become active until a con- 
siderable water-supersaturation is attained but they 
are still classed as condensation nuclei. Until more in- 
formation is available it would seem preferable to 
call all nuclei on which ice forms below water-saturation 
sublimation nuclei. It is conceded that the deposition 
of the first few molecular layers on such a nucleus may 
not be in the form of ice, but little is known about this. 
There is certainly a clear physical difference between 
ice crystals formed in this way and those which are 
formed by the freezing of a liquid drop which has 
already attained cloud drop size. In the latter case it is 
evident that a freezing nucleus is involved. 

On the basis of the definitions given above, it appears 
that a few sublimation nuclei which are active at 
temperatures as high as say — IOC exist in the atmos- 
phere. The failure to find these nuclei in the small ex- 



pansion chambers may be attributed to their low con- 
centration. Such low concentrations are adequate and 
even requisite for the release of precipitation by the 
ice-crystal mechanism. The evidence is that the large 
number of ice crystals found in surface air at — 32C and 
in cleaned air at — 41C are formed on freezing nuclei 
rather than on sublimation nuclei. There may also be 
freezing nuclei in the atmosphere which are active at 
much higher temperatures than — 32C. In some cases 
these may be solid condensation nuclei, or they may be 
picked up by collision after the drops are formed. 

PRECIPITATION PROCESSES 

It has been realized for some time that precipitation 
elements cannot be formed by a continuation of the 
processes of cloudy condensation, but that other physi- 
cal processes are necessary. In general, cloudy condensa- 
tion leads to the formation of a high concentration of 
small particles. The precipitation process must convert 
this multitude of small particles into a smaller number 
of much larger elements. Since the mass of a raindrop 
of 1-mm diameter is one million times that of a cloud 
drop of 10-M diameter, any proposed precipitation mech- 
anism must be capable of causing the rapid combination 
of large numbers of cloud elements. 

In a classic paper, Bergeron [4] reviewed the possible 
precipitation mechanisms and concluded that the only 
one of importance was the colloidal instability of a 
mixed water-ice cloud at- temperatures below OC. As is 
well known, the vapor pressure over water is greater 
than that over ice, at temperatures below freezing. 
The introduction of a few ice crystals into a super- 
cooled water cloud will result in the relatively rapid 
growth of the ice crystals at the expense of the super- 
cooled waterdrops. This idea was expanded and ex- 
tended by others, particularly by Findeisen [13]. Vari- 
ous theories were offered to explain the appearance of 
the necessary ice crystals in the supercooled cloud. 
Findeisen's proposal of sublimation nuclei was once 
accepted as best explaining the observed phenomena 
but is now questioned for the reasons already discussed. 
The substitution of freezing nuclei would not alter 
Findeisen's theory in any important respect. 

The ice-crystal theory of precipitation was widely 
accepted, since it seemed to be in accord with observa- 
tional evidence. The proponents of the theory cate- 
gorically stated that all moderate-to-heavy precipita- 
tion was initiated in this fashion and that, at most, only 
drizzle-type precipitation could fall from clouds which 
did not contain ice crystals. This conclusion was based 
largely on the observations that the precipitating clouds 
of middle latitudes extend above the freezing level and 
that much of the precipitation reaching the ground as 
rain is melted snow. The most common and apparently 
conclusive evidence is the glaciation of cumulonimbus 
prior to the release of precipitation. 

It has now been established that many low-latitude 
clouds which release moderate to heavy precipitation 
are entirely below the freezing level. This shows that 
there is another mechanism for the release of precipita- 
tion but does not invalidate the ice-crystal theory of 



176 



CLOUD PHYSICS 



precipitation for those clouds which extend above the 
freezing level. In the past the extension of a precipitat- 
ing cloud above the freezing level has been taken as 
evidence for the operation of the ice-crystal process. 
In view of the existence of nonsupercooled precipitating 
clouds a more rigorous criterion must be adopted. It 
cannot be assumed that the ice-crystal process is operat- 
ing luiless it can be established that ice crystals and 
supercooled drops are coexistent. 

The only other precipitation process worthy of serious 
consideration is the coalescence of drops in the gravita- 
tional field. If the drops are of nonuniform size, colli- 
sions will result because of their different terminal 
velocities of fall. The rate of growth by this process is 
dependent on the size and size distribution of the drops 
and on their concentration. Findeisen [14] studied this 
process in a cloud chamber and found that the resultant 
growth corresponded closely to what would be expected 
if each di-op coalesced with all drops in its path. Fin- 
deisen 's measurements were relatively crude and could 
not reveal the collection efficiency of one drop for 
slightly smaller drops. More recently, Langmuir [34] 
has computed the efficiency of collection of small drops 
by larger drops. The details of these computations are 
not presented in the reference but it is believed that the 
results are not completely reliable when the collecting 
and collected drops are of nearly the same size. In 
these computations it was assumed that the drops will 
coalesce if brought into physical contact; the collection 
efficiency is determined by the aerodynamic forces 
which tend to cause the smaller drops to follow the 
air streamlines around the larger drop. 

An intelligent appraisal of the two precipitation pro- 
cesses outlined above must be predicated on a quantita- 
tive analysis. Unfortimately, few such analyses have 
been made, and indeed many of the requisite data are 
lacking. The ice-crystal theory involves a molecular 
diffusion process. An expression similar to equation (1), 
derived for the geometric shape of the ice crystal rather 
than of a sphere, is required to permit a quantitative 
discussion of this process. The solution of the diffusion 
equation for geometric forms approximating ice crystals 
has not been given. In an unpublished study, the writer 
has obtained a solution for a thin circular disc which 
might be a useful approximation to some ice-crystal 
forms. Under the rather severe limitations imposed by 
the lack of a suitable equation, only approximate results 
can be obtained. The time required for an ice crystal of 
mass equivalent to a sphere of 20-m diameter to grow 
to an equivalent sphere diameter of 200 /x is of the 
order of 5 to 10 minutes. It was assumed that the vapor 
was saturated with respect to water at the optimum 
temperature of about — 15C. To a fair degree of ap- 
proximation the time required for the growth of the 
crystal increases with the square of the equivalent 
sphere diameter. Thus the time required for a crystal 
to grow to a mass equivalent to that of a raindrop of 1 
mm diameter would be of the order of several hours. 
These numerical values are only approximate and are 
for the most favorable conditions of supersaturation 
with respect to ice. The ice-crystal effect is capable of 



producing crystals of mass comparable to drizzle ele- 
ments in a few minutes but an excessive time is ap- 
parently required to form crystals of mass comparable 
to raindrops. 

With the aid of Langmuir's computed collection 
efficiencies of drops by larger drops [34] it is a relatively 
straightforward task to compute the growth of drops 
by accretion in the gravitational field. Langmuir's paper 
is so recent that no such calculations have yet appeared 
in the literature. The writer has made a few preliminary 
calculations which will have to serve as the basis for 
the present discussion.- The problem was simplified by 
considering the growth of an initially somewhat larger 
drop falling through a homogeneous cloud. It will 
suffice to consider one example in which the diameter of 
the homogeneous cloud drops was assumed to be 20 /n, 
the liquid-water content 1 g m~', and the diameter of the 
larger drop 30 /i. The growth of the drop under these 
conditions is presented in Table IV. The relatively long 

Table IV. Growth of a Drop of Initial Diameter 30 ii. 

Falling through a Cloud of 20-m Drops 

Containing 1 g m"' Liquid Water 



Drop diameter (ji) 


Time (cumulative) 
(minutes) 


Distance fallen 
(cumulative) (meters) 


30 








40 


45 


65 


60 


74 


163 


100 


92 


322 


200 


105 


650 


500 


116 


1475 


1000 


123 


2675 



time required for the drop to grow to 100 /x, compared 
with the time required for it to grow from 100 to 200 
IX, is striking. The larger the falling drop is in relation to 
the smaller cloud drops, the more rapid the accretion 
process. Thus, this process is favored by a broad cloud 
drop-size distribution. The data in Table IV should be 
considered as examples and not as definitive numerical 
values. More refined computations, based on a typical 
drop-size distribution, should be made. 

The two precipitation mechanisms can now be com- 
pared on the basis of the approximate numerical results 
presented above. The ice-crystal effect is more rapid 
than the collision process in the initial stages and is 
independent of the drop-size distribution. In the latter 
stages of growth the collision mechanism is more rapid 
than the ice-crystal effect, and may also initiate pre- 
cipitation in clouds which do not contain ice crystals if 
the drop-size distribution is sufficiently broad. The 
two precipitation mechanisms taken together appear 
to be sufficient to explain the formation of precipita- 
tion. The Avriter's concept of the roles of the two 
processes is as follows: In all cases in which ice crystals 
are present, the ice-crystal process is dominant in the 
initiation of precipitation and in causing growth to an 
equivalent sphere diameter of the order of a few hun- 



2. Subsequent to the preparation of this article the writer 
has extended these calculations. They will be found in "A Pre- 
liminary Quantitative Analysis of Precipitation Mechanisms," 
by H. G. Houghton, J. Meteor., 7: 363-369 (1950). 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 



177 



dred microns. In the absence of ice crystals, the coUision 
mechanism may initiate the precipitation process if the 
drop-size distribution is broad. Regardless of the process 
of initiation, the fiu'ther growth of the precipitation 
elements is primarily by collision. This includes colli- 
sions of the precipitation elements with themselves as 
well as with cloud elements. In the case of snow, colli- 
sions between crystals are common, as is evidenced by 
even a casual examination of snowflakes. No process 
depending on the diffusion of water vapor seems to be 
capable of forming raindrops of 1-mm diameter and 
larger in the time available. Svich precipitation elements 
must be formed by a collision mechanism. In middle 
latitudes, it is probable that the collisions are primarily 
bet\\'een ice crystals, forming snowflakes which later 
melt into raindrops. In low latitudes, or in any situation 
in which a water-drop cloud, of large vertical extent 
exists, once drops of, for example, 100-// diameter 
appear, collision with the cloud drops is sufficient to 
explain the growth of the precipitation elements. More 
quantitative information on collision processes is badly 
needed, particularly on collisions between ice crystals 
and between cloud drops of nearly the same size. 

The question naturally arises as to why all clouds do 
not ultimately release precipitation as a result of colli- 
sions between drops of unequal size. It is well known 
that many clouds produce precipitation which evapo- 
rates before reaching the ground, but this is not the 
complete answer. Langmuir's computations [34] show 
that for each drop size there is a minimum size of the 
larger drop below which no collisions will occur. For 
example, no drop of less than 45-// diameter will collide 
with drops of 12-ix diameter. As the smaller drop diam- 
eter increases, the minimum diameter of the larger 
drop approaches that of the smaller drop. These results 
unfortunately lie in the region where the computations 
are least reliable. If correct, these results show that 
clouds composed of small drops are stable even when 
the drop-size distribution is broad. Diem's data [10] 
show that clouds such as fair-weather cumulus and 
stratocumulus contain smaller drops than clouds such 
as nimbostratus and heavy cumulus. Stratus also con- 
tains large drops but is not deep enough to yield more 
than drizzle. Houghton [20] and others have also sug- 
gested that a unipolar electric charge on the cloud 
drops might serve to inhibit collisions. 

Snow. For the most part the discussion above has 
assumed the initial presence of a water-drop cloud. 
It may be that snow is often initiated in this way, but 
it is probable that snow also occurs in the absence of a 
water cloud. Also, a water cloud will not ordinarily 
exist for more than a short time in the presence of 
snow. It has been stated earlier that ice crystals do 
not form until saturation with respect to water is 
approached. Apparently few freezing or sublimation 
nuclei are active at temperatures above — IOC, and 
lower temperatures are generally required. On the other 
hand, there is evidence that the top of a snow cloud 
may be warmer than —IOC. This suggests that once 
snow is initiated, nuclei are produced which are active 
at higher temperatures. An important contribution to 



this problem was made by Findeisen [15], who found 
that the more delicate forms of crystals (stellar or 
dendritic) shed tiny splinters of ice as they fall. These 
splinters would serve as sublimation nuclei for new 
crystals at any temperature below freezing. 

Approximate computations of the rate of growth of 
ice crystals suggest that the vapor pressure must be 
nearer saturation with respect to water than to ice if 
the observed sizes are to be attained. In this respect 
the process is quite different from condensation on 
liquid drops, where the vapor is only very slightly 
supersaturated with respect to the condensed phase. 
This chfference is due to the much smaller number of 
ice crystals. The supersaturation increases as required 
to cause sublimation to proceed at the rate prescribed 
by the lifting, saturation with respect to water setting 
the upper limit. 

Nakaya and collaborators in Japan [40, 41, 42] have 
made outstanding contributions to our knowledge of 
the formation of snow crystals. In one paper Nakaya 
and Terada [42] have presented useful data on the 
mass, physical dimensions, and velocity of fall of several 
types of natural snow crystals. In general, the maximum 
masses of the crystals are equivalent to a solid sphere 
of several hundred microns diameter while the velocities 
of fall are much smaller than those of solid spheres of 
equivalent mass. Nakaya and collaborators [40, 41] 
have succeeded in producing in the laboratory all of 
the types of crystals observed in nature. The two 
fundamental parameters determining the crystal type 
are temperature and degree of supersaturation. In gen- 
eral, the more compact crystal forms such as columns, 
prisms, and plates are formed at low supersaturations 
and the more open types such as needles and stellar 
or dendritic crystals are formed at the higher super- 
saturations. The dependence on temperature was not 
clearly established in the references, all of which were 
published before World War II. Dr. Nakaj^a was able 
to continue his researches during and after the war, 
but these results have been published only in Japanese. 
However, he has prepared all of his material in book 
form in English, and early publication is anticipated. 

Weickmann [55] collected and photographed ice crys- 
tals in the free atmosphere. He summarized his ob- 
servations as follows: In the lower troposphere, the 
nimbostratus region, there is slight ice supersaturation, 
the temperature ranges from to — 15C, and the 
crystals are in the form of thin plates and stars; in the 
middle troposphere or the altocumulus and altostratus 
region, there is moderate ice supersaturation, the tem- 
perature ranges from —15 to — 30C, and the crystals 
are mainly thick plates and prisms; in the cirrus region 
or the upper troposphere, the temperature ranges from 
— 30 to — 60C, and the ice crystals are principally 
hollow prisms often combined as twins or clusters. 

Size of Raindrops. All of the published data on rain- 
drop .size were obtained at the surface. A considerable 
numlier of such measurements have been published but 
it will suffice to refer to the rather recent measurements 
of Laws and Parsons [36]. They used the flour-pellet 
technique and found that the \'olume-median diameter 



178 



CLOUD PHYSICS 



increased with rainfall intensity. For a rainfall rate of 
0.05 in. hr~' they give a volume-median diameter of 1.1 
mm with a maximum diameter of 4 mm; for 0.5 in. hr~^ 
the volume-median diameter was 1 .9 mm and the maxi- 
mum diameter was 5.5 mm; for 4.0 in. hr~^ the volume- 
median diameter was 2.8 mm and the maximum di- 
ameter was 6.7 mm. The size and size distribution of 
raindrops can be expected to change from the cloud 
base to the ground because of evaporation, coalescence of 
drops, the variation of time of fall with drop size, and 
the fracture of large drops. For studies of the precipita- 
tion process it would be necessary to measure the rain- 
drop size in and immediately below the cloud. 

Hail. Hail is a special type of frozen precipitation 
associated with thunderstorms and characterized by 
extreme sizes much in excess of those of any other 
precipitation elements. A typical hailstone exhibits an 
onionlike structure when dissected, which has given 
rise to the belief that hailstones are formed by repeated 
excursions above and below the freezing level whereby 
successive layers of water are frozen onto it. A natural 
consequence of this theory was the inference that verti- 
cal velocities equalling the free-fall velocities of the 
hailstones exist in the atmosphere (over 100 mph in 
some cases). 

It is now generally accepted that the major growth 
of the hailstone is by the collection of supercooled water 
as the stone falls relative to the cloud. In the earlier 
stages the stone may well travel in a very irregular 
fashion, up as well as dowTi, but the largest hailstones 
can hardly be supported by updrafts. The growth of 
the hailstone is essentially the same as the accretion of 
ice on aircraft. The layer structure is due to inhomo- 
geneities in the turbulent cloud. A similar layer struc- 
ture is commonly observed in ice deposits on aircraft. 
Large hailstones are favored by high vertical velocities, 
a large vertical extent of the supercooled portion of 
the cloud, and high liquid-water content. Schumann 
[47] has shown that the extreme values of these param- 
eters associated ^vith cumulonimbus can lead to hail- 
stones of the observed sizes. Hailstones large enough 
to damage aircraft have been reported in the clear air 
surrounding a thunderstorm, suggesting that stones for 
example, of one or two centimeters diameter may be 
discharged from the tops of thunderclouds. The termi- 
nal velocities of hailstones of 1 and 2 cm diameter are 
about 12 and 16 m sec~^ respectively. Extreme thunder- 
storm updrafts may readily exceed these velocities. 
Regardless of their direction of travel with respect to 
the earth, the hailstones are moving downward through 
the supercooled water drops at their terminal velocities. 
The thunderstorm updraft serves primarily to increase 
•the length of the hailstone's path through the cloud 
and therebjr to increase its collection of ice. 

ARTIFICAL DISSIPATION OF FOG 

Although fog hampers all types of transportation, its 
effects on air transportation are most serious. Much of 
the impetus for the development of methods for arti- 
ficial dissipation of fog has come from aviation interests. 
Many unsuccessful attempts have been made to dis- 



sipate fog, failure being due in most cases to a lack of 
understanding of the problem. Some successful experi- 
ments were not followed up because it was believed 
that instrument-landing systems would make fog dissi- 
pation unnecessary. With the advent of World War II 
the problem became acute, and the British developed 
a thermal method now called "Fido." This system has 
been developed further, since the war, both in England 
and in the United States where an operational installa- 
tion has recently been made at a commercial air field. 
In spite of continued advances in instrument-landing 
systems, most operators still feel that a cleared region 
for the final touchdown would greatly increase the 
safety of the landing. It seems evident that instrument- 
landing techniques will eventually be developed to the 
point where fog dissipation is completely unnecessary, 
but the writer would not care to speculate as to when 
this will come to pass. 

In general, fog can be dispelled by the evaporation of 
the drops or by the physical removal of the drops from 
the air. Most of the methods for accomplishing this 
have been discussed critically by Houghton and Rad- 
ford [23]. Those methods which were considered reason- 
ably feasible were (1) the direct application of heat, (2) 
the use of hygroscopic materials to "dry" the air, and 
(3) the dropping of electrically-charged particles 
through the fog. The first method is exemplified by 
"Fido," in which heat is released by the burning of oil 
in long lines of burners on either side of the runway. 
The second method was used successfully by Houghton 
and Radford. The third method was experimented with 
by Warren, who dropped charged sand on clouds with 
occasional success. 

There is now no doubt that fog can be dispelled by 
artificial means. Further experimentation with methods 
already proved practicable is desirable and there is still 
room for new ideas in both methods and equipment. 
The basic problem lies in the economics of fog dispersal. 
The mass of suspended water to be dealt with in even a 
relatively small volume is large, and it is inevitable that 
relatively large expenditures of energy will be required 
to remove it. As an example, the mass of water over an 
airport runway 6000 ft long and 300 ft wide to a height 
of 200 ft is about one to two tons, depending on the 
liquid-water content of the fog. In order to dissipate the 
fog by evaporation it is necessary both to supply the 
latent heat of vaporization and to lower the relative 
humidity of the air to cause the drops to evaporate 
rapidly. It is generally necessary to reduce the relative 
humidity to 90-95 per cent to meet the latter require- 
ment. The heat energy required to evaporate the water- 
drops and to reduce the relative humidity to 90 per 
cent in a fog at IOC, containing 0.1 g m~' of liquid 
water, is about 559 cal m~'. Of this amount, nearly 500 
cal m~' are required to reduce the relative humidity of 
the air. 

If we use the figures above, a total of some 5.7 X 10^ 
cal would be required to clear the fog in the volume 
assumed above. This rather impressive number of calo- 
ries can be supplied by burning the modest amount of 
250 gal of oil at a combustion efficiency of about 70 



ON THE PHYSICS OF CLOUDS AND PRECIPITATION 



179 



per cent. The computed energy requirement is for 
optimum conditions whicli cannot be realized in prac- 
tice. Even a liglit wind steadily brings in more fog, 
so that the heating must be continuous. It is not 
practicable to apply the heat uniformly, and in practice 
much of the heat is wasted in raising the temperature 
of some of the air much higher than is necessary. The 
concentrated heat sources produce convection currents 
which may carry the heat to unwanted heights and 
suck in additional fog from the sides. For these reasons 
the practical energy requirements are many times the 
computed minimum. Working installations are designed 
to burn on the order of 100,000 gal of oil per hour. 

Methods utilizing hygroscopic materials to dissipate 
fog are also evaporative processes and the basic energy 
requirements are the same as for the heating methods. 
Experiments reported by Houghton and Radford [23] 
indicate that operating systems require from five to ten 
times the theoretical minimum quantities of hygro- 
scopic material. 

Methods of physical removal of the fog drops, such 
as the charged-sand process, have smaller theoretical 
energy requirements than the evaporation methods. 
No basic energy requirement comparable to that given 
for the evaporative methods can be set and no experi- 
mental values are available. 

The two evaporative methods which have been sub- 
jected to full-scale tests, namely the burning oil and 
hygroscopic material methods, are demonstrably ca- 
pable of producing clearings of useful size. In both 
cases the costs of operation are relatively high and 
extensive installations are required. The use of hygro- 
scopic materials involves the hazards of corrosion and 
damage to electrical equipment, although these may 
be nearly eliminated by proper design. The existence 
of large oil burners along the sides of the runway is a 
potential hazard which can also be minimized by proper 
design. Because of cost and other practical considera- 
tions only limited clearings are feasible, so that auxil- 
iary instrumental methods must be available to guide 
the aircraft into the clearing. Neither method can deal 
with other conditions of poor visibility, such as dense 
snow, smoke, and dust. It must be concluded that fog 
dissipation by these methods is economically marginal 
and that installations are justifiable only in locations of 
extreme fog frequency or for urgent military purposes. 

The fact that all proved methods of fog dissipation 
require much more energy than the theoretical mini- 
mum offers some hope that more efficient methods can 
be found. There is certainly room for further work on 
methods such as the electrified-sand technique where 
there is reason to believe that the energy requirements 
are more modest. The ever-recurrent hope that a 
method will be found which will clear large areas of 
fog with the expenditure of small amounts of energy is 
incompatible with physical reality. 

CONCLUSIONS AND RECOMMENDATIONS 

Our present understanding of the physics of con- 
densation and precipitation is incomplete in many im- 
portant areas. The writer has attempted to point out 



deficiencies in each phase of the subject during the 
detailed discussion. It is hoped that this will be of value 
to the reader, but it is felt that a more general ap- 
praisal of the situation is in order. In particular, an 
attempt will be made to present the writer's views as to 
the relative importance of those phases of the subject 
which need further study. This requires a decision as to 
the most important contribution to meteorology as a 
whole which can be expected from the study of cloud 
physics. The author feels that the complete explanation 
of precipitation should be the dominant aim of the 
cloud physicist. Of the elements forecast, precipitation 
is probably the most important to the majority of 
people. Further, the complete explanation of the pre- 
cipitation process involves a knowledge of most of the 
topics in cloud physics. In making this decision the 
writer is acutely aware of the possibility that some new 
discovery will necessitate a refocusing of the entire 
cloud physics program. 

Knowledge of condensation nuclei and of condensa- 
tion in the liquid phase is incomplete in detail but is 
relatively satisfactory as compared to other parts of 
the field. The most important problem in this area is 
the investigation of the factors determining the breadth 
of the drop-size distribution. Knowledge of the ice 
phase in the atmosphere is inadequate. It is imperative 
that the nature and mode of action of freezing nuclei 
and sublimation nuclei be determined. This information 
is essential to an evaluation of and practical utilization 
of the ice-crystal theory of precipitation. It is equally 
imperative that a complete study be made of the 
growth of drops by collision in the gravitational field. 

It is the writer's opinion that these problems should 
be attacked experimentally both in the laboratory and 
in the free atmosphere. The mechanisms of phase 
changes can be studied only in the laboratory, and the 
collision process is also a proper subject for laboratory 
investigation. However, the most complete laboratory 
stud}'' will not tell us what is happening in the atmos- 
phere. It is therefore essential that flight measurements 
be made to determine which precipitation process oper- 
ates under various conditions and to obtain a quantita- 
tive verification of the operation of the assumed proc- 
esses. No adequate instrumentation is available for 
flight observations, and instrument development is 
therefore an essential part of the program. Flight meas- 
urements are extremely costly and time-consuming and 
should not be embarked on without careful planning 
and adequate instrumentation. 

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180 



CLOUD PHYSICS 



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NUCLEI OF ATMOSPHERIC CONDENSATION^" 

By CHRISTIAN JUNGE 
Meteorological Institute for Northwestern Germany 



The Condensation feffect of the Nuclei 

According to Wall [38], the condensation effect of a 
nucleus can be compared to that of a droplet of pure 
water on which, because of the surface curvature, con- 
densation will take place only when there is a definite 
amount of supersaturation (Thomson's equation). The 
following distinctions between different types of nuclei 
can then be made: 

1. Particles insoluble in water and unwettable. These 
may serve, as tests have shown [20], as nuclei of con- 
densation. They require (when spherical) a larger 
amount of supersaturation than do droplets of pure 
water. Their importance for the natural aerosol is slight. 

2. Particles insoluble in water, but wettable. Accord- 
ing to the existing humidity and to their degree of 
wettability, these particles are surrounded by one or 
more molecular layers [40] of adsorbed water. They 
begin to condense at, or somewhat below, the value 
given by Thomson's equation. If these particles are of 
irregular or flaky structure, condensation begins before 
saturation, either in cavities (as capillary condensation) 
or in porous nuclear substances (as absorption of water) . 

3. Droplets of solutions. These form an important 
group of nuclei. Owing to the dissolved substance, the 
degree of supersaturation necessary for condensation 
falls to as low a value as J^ of that indicated by Thom- 
son's formula [25]. 

Between particles of types 2 and 3 there are many 
intermediate types, because, as a result of coagulation, 
many nuclei will contain both soluble and insoluble 
matter (mixed nuclei). Figure 1 shows the relationship 
between the radius of the nuclei and the amount of 
supersatui-ation necessary for condensation to occur. 
It is evident that, in the presence of condensation 
nuclei, the range of supersaturation necessary for the 
formation of clouds extends from to about 20 per 
cent. 

The processes of condensation on nuclei at tempera- 
tures below OC, which have recently been the object of 
thorough research, will be mentioned only briefly here, 
because they represent a transition into the field of 
cloud physics [27]. Weickmann [41] found that the 
nuclei act fundamentally as condensation nuclei for the 
liquid phase even at temperatures below freezing, that 
is, only at saturation with respect to watei- does con- 
densation take place in the form of droplets, some of 
which may subsequently freeze. Sublimation nuclei, in 
the sense of Bergeron-Findeisen, which may form ice 
particles already at supersaturation with respect to ice, 
seem to exist only in negligible quantities, if at all. 

According to Laf argue [22], the droplets initially 
formed freeze at about — 41C in the size range between 



* Translated from the original German. 



1 yu and 20 fi, rather independently of the presence of 
dissolved substances. Heverly [13] found that this spon- 
taneous freezing point rises to — 16C for drops of 0.4 
mm diameter and then remains constant for drops up 
to about one mm diameter, likeAvise largely independ- 
ently of the source of the water. However, according to 
Weickmann, the presence of certain solid particles, so- 
called freezing nuclei, appears to modify these processes 
by raising the freezing point. This modification depends 
on the size and nature of the freezing nuclei. 

Size, Number of Nuclei, and Methods of Measurement 

If we disregard the small ions (radius r pa 10~' cm), 
which are not of interest here, the size range of con- 
densation nuclei extends approximately from r = 4 X 
10~' to lO"* cm (Fig. 1). Although all tj^pes of particles 
may be active as condensation nuclei in a nuclei counter 
(see next paragraph and [20]), only those nuclei which 
require the lowest degi-ee of supersaturation (i.e., haze 
droplets and large nuclei droplets) are active in the 
actual atmosphere. It is within this group of particles 
— recently re-examined by Dessens [8, 9] and Woodcock 
and Gifford [43] — that we find the real meteorological 
condensation nuclei. By what method, now, can we 
measure these particles which range in size over three 
orders of magnitude? 

All nuclei, whether hygroscopic or even unwettable, 
with radii ranging from about 4 X 10~^ to 2 X 10~^ 
cm, are counted in nuclei counters, so called after Aitken 
[3, 23]. The lower limit of this range is determined by 
the ratio of expansion; however, it appears that the 
values of supersaturation computed from this ratio are 
substantially too high [17]. The upper limit — ^which is 
highly uncertain — can be established with a certain 
degree of probability by assuming that larger nuclei 
droplets grow so rapidly in the saturated air of the 
counting chamber that they are probably precipitated 
before the actual measurement (Fig. 3). This seems to 
be corroborated by the photographs of condensation 
nuclei taken with an electron m